標(biāo)題: Titlebook: Elementary Topics in Differential Geometry; J. A. Thorpe Textbook 1979 Springer-Verlag New York Inc. 1979 Differentialgeometrie.Isometrie. [打印本頁(yè)] 作者: cobble 時(shí)間: 2025-3-21 16:52
書(shū)目名稱(chēng)Elementary Topics in Differential Geometry影響因子(影響力)
書(shū)目名稱(chēng)Elementary Topics in Differential Geometry影響因子(影響力)學(xué)科排名
書(shū)目名稱(chēng)Elementary Topics in Differential Geometry網(wǎng)絡(luò)公開(kāi)度
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書(shū)目名稱(chēng)Elementary Topics in Differential Geometry被引頻次
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書(shū)目名稱(chēng)Elementary Topics in Differential Geometry讀者反饋
書(shū)目名稱(chēng)Elementary Topics in Differential Geometry讀者反饋學(xué)科排名
作者: MIRE 時(shí)間: 2025-3-21 20:43
The Gauss Map,on .:. → ?.. associated with the vector field . by .(.) = (., .(.)), . ∈ ., actually maps . into the unit .-sphere S. ? ?.. since ∥.(.)∥ = 1 for all . ∈ .. Thus, associated to each oriented .-surface . is a smooth map .: . → S.. called the .. . may be thought of as the map which assigns to each poin作者: ENNUI 時(shí)間: 2025-3-22 02:57
Geodesics, proccss of differentiation of vector fields and functions defined along parametrized curves. In order to allow the possibility that such vector fields and functions may take on different values at a point where a parametrized curve crosses itself, it is convenient to regard these fields and functio作者: Coronation 時(shí)間: 2025-3-22 06:30
Parallel Transport,however, generally not tangent to .. We can, nevertheless, obtain a vector field tangent to . by projecting ?(.) orthogonally onto .. for each . ∈ . (see Figure 8.1). This process of differentiating and then projecting onto the tangent space to . defines an operation with the same properties as diff作者: Gum-Disease 時(shí)間: 2025-3-22 10:31 作者: 金桌活畫(huà)面 時(shí)間: 2025-3-22 13:27 作者: 金桌活畫(huà)面 時(shí)間: 2025-3-22 20:06
Convex Surfaces,ee Figure 13.1). An oriented .-surface . is . at . ∈ . if there exists an open set . ? ?.. containing . such that . ∩ . is contained either in . or in .. Thus a convex .-surface is necessarily convex at each of its points, but an .-surface convex at each point need not be a convex .-surface (see Fig作者: languid 時(shí)間: 2025-3-22 23:24
Parametrized Surfaces,ure . and (ii) define various integrals over .. We shall now carry out a similar program for .-surfaces (. > 1). It will turn out that oriented .-surfaces (even connected ones) in general admit only local parametrizations, but that will be adequate for our needs.作者: 濕潤(rùn) 時(shí)間: 2025-3-23 02:04 作者: 陰郁 時(shí)間: 2025-3-23 06:50
The Exponential Map, We begin by using a technique of the calculus of variations analogous to the one we used in Chapter 18 to study minimal surfaces. Now, however, we shall vary parametrized curves rather than parametrized surfaces作者: Euthyroid 時(shí)間: 2025-3-23 11:12
The Gauss Map, ∈ .. Thus, associated to each oriented .-surface . is a smooth map .: . → S.. called the .. . may be thought of as the map which assigns to each point . ∈ . the point in ?.. obtained by “translating” the unit normal vector .(.) to the origin (see Figure 6.1).作者: adduction 時(shí)間: 2025-3-23 16:48 作者: PANG 時(shí)間: 2025-3-23 19:04
Parallel Transport,see Figure 8.1). This process of differentiating and then projecting onto the tangent space to . defines an operation with the same properties as differentiation, except that now differentiation of vector fields tangent to . yields vector fields tangent to .. This operation is called covariant differentiation.作者: Infelicity 時(shí)間: 2025-3-24 01:28 作者: 攝取 時(shí)間: 2025-3-24 06:22 作者: SMART 時(shí)間: 2025-3-24 07:58 作者: 廢墟 時(shí)間: 2025-3-24 12:56
https://doi.org/10.1007/978-1-84628-551-6s and functions may take on different values at a point where a parametrized curve crosses itself, it is convenient to regard these fields and functions to be defined on the parameter interval rather than on the image of the curve.作者: 維持 時(shí)間: 2025-3-24 16:00 作者: 臨時(shí)抱佛腳 時(shí)間: 2025-3-24 20:53
Focal Points,it follows that . that is, the curve . pauses (has velocity zero) at . = .. Geometrically, this says that the normal lines which start along the curve ? ° α near ?(.) = ?(α(.)) tend to focus at . = ?.(α(.)) = ?.(.) (see Figure 16.1). Such points . are called . of ?. Note that the normal lines along α need not actually meet at a focal point.作者: GEM 時(shí)間: 2025-3-25 01:39
Textbook 1979es. This has been brought about by the introduction of linear algebra into the curriculum at the sophomore level. The advantages of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. Several textbooks adoptin作者: Expressly 時(shí)間: 2025-3-25 06:55 作者: OTHER 時(shí)間: 2025-3-25 10:32
0172-6056 nt books do use linear algebra, it is only the algebra of ~3. The student‘s preliminary understanding of higher dimensions is not cultivated.978-1-4612-6155-1978-1-4612-6153-7Series ISSN 0172-6056 Series E-ISSN 2197-5604 作者: 不朽中國(guó) 時(shí)間: 2025-3-25 14:05 作者: Foment 時(shí)間: 2025-3-25 17:03 作者: Arrhythmia 時(shí)間: 2025-3-25 22:02
How People View Computing Today,on .:. → ?.. associated with the vector field . by .(.) = (., .(.)), . ∈ ., actually maps . into the unit .-sphere S. ? ?.. since ∥.(.)∥ = 1 for all . ∈ .. Thus, associated to each oriented .-surface . is a smooth map .: . → S.. called the .. . may be thought of as the map which assigns to each poin作者: innovation 時(shí)間: 2025-3-26 01:47
https://doi.org/10.1007/978-1-84628-551-6 proccss of differentiation of vector fields and functions defined along parametrized curves. In order to allow the possibility that such vector fields and functions may take on different values at a point where a parametrized curve crosses itself, it is convenient to regard these fields and functio作者: SEVER 時(shí)間: 2025-3-26 06:54
https://doi.org/10.1057/9781137313676however, generally not tangent to .. We can, nevertheless, obtain a vector field tangent to . by projecting ?(.) orthogonally onto .. for each . ∈ . (see Figure 8.1). This process of differentiating and then projecting onto the tangent space to . defines an operation with the same properties as diff作者: NEG 時(shí)間: 2025-3-26 10:32
,Treatment 1—Therapeutic Materials,r transformation on the 1-dimensional spacc .. Sincc every linear transformation from a 1-dimensional space to itself is multiplication by a real number, there exists, for each . ∈ ., a real number .(p) such that .. K(.) is called the . of . at ..作者: 中子 時(shí)間: 2025-3-26 16:14 作者: 享樂(lè)主義者 時(shí)間: 2025-3-26 19:06
https://doi.org/10.1007/978-1-4615-8744-6ee Figure 13.1). An oriented .-surface . is . at . ∈ . if there exists an open set . ? ?.. containing . such that . ∩ . is contained either in . or in .. Thus a convex .-surface is necessarily convex at each of its points, but an .-surface convex at each point need not be a convex .-surface (see Fig作者: 發(fā)誓放棄 時(shí)間: 2025-3-26 22:59 作者: nutrition 時(shí)間: 2025-3-27 01:53
Living with Wildlife in Zimbabweigure 15-6). When . = 0, ?. = ? is a parametrized .-surface in ?... For . ≠ 0. however, ?. may fail to be a parametrized .-surface because there may be points . ∈ . at which ?. fails to be regular. At each such point there will be a direction . such that .. If α is a parametrized curve in . with ., 作者: 放逐某人 時(shí)間: 2025-3-27 06:57
We begin by using a technique of the calculus of variations analogous to the one we used in Chapter 18 to study minimal surfaces. Now, however, we shall vary parametrized curves rather than parametrized surfaces作者: Legend 時(shí)間: 2025-3-27 10:26 作者: Mitigate 時(shí)間: 2025-3-27 15:04
Elementary Topics in Differential Geometry978-1-4612-6153-7Series ISSN 0172-6056 Series E-ISSN 2197-5604 作者: 叢林 時(shí)間: 2025-3-27 18:40
,Treatment 1—Therapeutic Materials,r transformation on the 1-dimensional spacc .. Sincc every linear transformation from a 1-dimensional space to itself is multiplication by a real number, there exists, for each . ∈ ., a real number .(p) such that .. K(.) is called the . of . at ..作者: 偶然 時(shí)間: 2025-3-28 01:01
Living with Nature, Cherishing Languageeasures the turning of the normal as one moves in S through . with various velocities .. Thus . measures the way . curves in ?.. at .. For . = 1, we have seen that . is just multiplication by a number .(p) the curvature of . at .. We shall now analyze . when . > 1.作者: 運(yùn)動(dòng)性 時(shí)間: 2025-3-28 06:01
https://doi.org/10.1007/978-1-4615-8744-6ee Figure 13.1). An oriented .-surface . is . at . ∈ . if there exists an open set . ? ?.. containing . such that . ∩ . is contained either in . or in .. Thus a convex .-surface is necessarily convex at each of its points, but an .-surface convex at each point need not be a convex .-surface (see Figure 13.2).作者: 牛馬之尿 時(shí)間: 2025-3-28 10:18 作者: 嚴(yán)重傷害 時(shí)間: 2025-3-28 13:47 作者: 河流 時(shí)間: 2025-3-28 15:37 作者: conspicuous 時(shí)間: 2025-3-28 20:51
Curvature of Surfaces,easures the turning of the normal as one moves in S through . with various velocities .. Thus . measures the way . curves in ?.. at .. For . = 1, we have seen that . is just multiplication by a number .(p) the curvature of . at .. We shall now analyze . when . > 1.作者: Inflamed 時(shí)間: 2025-3-29 02:07
Convex Surfaces,ee Figure 13.1). An oriented .-surface . is . at . ∈ . if there exists an open set . ? ?.. containing . such that . ∩ . is contained either in . or in .. Thus a convex .-surface is necessarily convex at each of its points, but an .-surface convex at each point need not be a convex .-surface (see Figure 13.2).作者: 輕彈 時(shí)間: 2025-3-29 05:57 作者: 顯而易見(jiàn) 時(shí)間: 2025-3-29 09:06 作者: 無(wú)力更進(jìn) 時(shí)間: 2025-3-29 14:28 作者: 支架 時(shí)間: 2025-3-29 18:07
https://doi.org/10.1007/978-1-349-18756-0The tool which will allow us to study the geometry of level sets is the calculus of vector fields. In this chapter we develop some of the basic ideas.作者: 閃光你我 時(shí)間: 2025-3-29 23:42
Let .: . → ? be a smooth function, where . ? ?.. is an open set. let . ∈ ? be such that .(.) is non-empty, and let . ∈ .(.). A vector at . is said to be . .(.) if it is a velocity vector of a parametrized curve in ?.. whose image is contained in .(.) (see Figure 3.1).作者: 摸索 時(shí)間: 2025-3-30 00:26
Paul Kamudoni,Nutjaree Johns,Sam SalekA .. in ?.. is a non-empty subset . of ?.. of the form . = .(.) where .: . → ?, . open in ?.. is a smooth function with the properly that ?.(.) ≠ . for all . ∈ .. A 1-surfacc in ?. is also called a .. A 2-surface in ?. is usually called simply a .. An .-surface in ?.. is often called a .. especially when . > 2.作者: 燦爛 時(shí)間: 2025-3-30 05:28
In Search of a New Left, Then and Now,A . . . . ? ?. is a function which assigns to each point . in . a vector .(.) ∈ ? . at .. If .(.) is tangent to . (i.e., .(.) ∈ .) for each . ∈ ., . is said to be a . on .. If .(.) is orthogonal to . (i.e.. .(.) ∈ .) for each . ∈ ., . is said to be a . (see Figure 5.1).作者: Congestion 時(shí)間: 2025-3-30 10:23
Clotting Factor Antibodies (Inhibitors),We shall now consider the local behavior of curvature on an .-surface. The way in which an .-surface curves around in ?.. is measured by the way the normal direction changes as we move from point to point on the surfacc. In order to measure the rate of changc of the normal direction, we need to be able to differentiate vector fields on .-surfaces.作者: 不怕任性 時(shí)間: 2025-3-30 12:49 作者: Nucleate 時(shí)間: 2025-3-30 16:56
https://doi.org/10.1007/978-1-4614-3752-9In this chapter we shall establish two theorems which show that, locally, .-surfaces and parametrized .-surfaces are the same. In order to do this, we will need to use the following theorem from the calculus of several variables.作者: 卜聞 時(shí)間: 2025-3-30 23:43
Dale Salwak (Professor of English)We consider now the problem of how to find the volume (area when . = 2) of an .-surface in ?... As with the length of plane curves, this is done in two steps. First we define the volume of a parametrized .-surface and then we define the volume of an .-surface in terms of local parametrizations.作者: fatuity 時(shí)間: 2025-3-31 01:19
Haemodialysis — a personal viewpointLet ?: . → ?.. be a parametrized .-surface in ?... A . of ? is a smooth map .: . x (??, ?) → ?.. with the property that .(.,0) = ?(.) for all . ∈ .. Thus a variation surrounds the .-surface ? with a family of singular .-surfaces ?.: . → ?.. (?? < ? < ?) defined by ? . (.) = .(., .).作者: Notorious 時(shí)間: 2025-3-31 06:18
Vector Fields,The tool which will allow us to study the geometry of level sets is the calculus of vector fields. In this chapter we develop some of the basic ideas.作者: nullify 時(shí)間: 2025-3-31 09:16 作者: 過(guò)分自信 時(shí)間: 2025-3-31 13:37 作者: 發(fā)展 時(shí)間: 2025-3-31 19:39 作者: Relinquish 時(shí)間: 2025-4-1 00:53 作者: Alienated 時(shí)間: 2025-4-1 02:59
