An Introduction to Differentiable Manifolds and Riemannian GeometryAcademic Press, 1986/04/21 - 429 ページ An Introduction to Differentiable Manifolds and Riemannian Geometry |
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viii ページ
... Parameter and Local One-Parameter Groups Acting on a Manifold 123 The Existence Theorem for Ordinary Differential Equations 131 Some Examples of One-Parameter Groups Acting on a Manifold 139 One-Parameter Subgroups of Lie Groups 147 The ...
... Parameter and Local One-Parameter Groups Acting on a Manifold 123 The Existence Theorem for Ordinary Differential Equations 131 Some Examples of One-Parameter Groups Acting on a Manifold 139 One-Parameter Subgroups of Lie Groups 147 The ...
xiv ページ
... parameter subgroup. In the last two chapters, which deal with Riemannian geometry of abstract n-dimensional manifolds, the relation to the more easily visualized geometry of curves and surfaces in Euclidean space is carefully spelled ...
... parameter subgroup. In the last two chapters, which deal with Riemannian geometry of abstract n-dimensional manifolds, the relation to the more easily visualized geometry of curves and surfaces in Euclidean space is carefully spelled ...
xv ページ
... parameter group action. In Chapter V covariant tensors and differential forms are treated in some detail and then used to develop a theory of integration on manifolds in Chapter VI. Numerous applications are given. It would be possible ...
... parameter group action. In Chapter V covariant tensors and differential forms are treated in some detail and then used to develop a theory of integration on manifolds in Chapter VI. Numerous applications are given. It would be possible ...
16 ページ
... parameters: two being the Figure I.7 local coordinates of p relative to some coordinate neighborhood U. The 2-sphere S4 and some of its tangent vectors—elements of T(S*). the derivatives 6g/6x', ..., 6g/6x" all being evaluated at the. 16 ...
... parameters: two being the Figure I.7 local coordinates of p relative to some coordinate neighborhood U. The 2-sphere S4 and some of its tangent vectors—elements of T(S*). the derivatives 6g/6x', ..., 6g/6x" all being evaluated at the. 16 ...
72 ページ
... parameter in the previous example: Let g(t) be a monotone increasing C* function on — oc < t < 00 such that g(0) = st, lim, ... g(t) = 0 and lim, ... g(t) = 2it. For example, we may use g(t) = 1 + 2 tan't. Then G(t) is given by ...
... parameter in the previous example: Let g(t) be a monotone increasing C* function on — oc < t < 00 such that g(0) = st, lim, ... g(t) = 0 and lim, ... g(t) = 2it. For example, we may use g(t) = 1 + 2 tan't. Then G(t) is given by ...
目次
1 | |
20 | |
51 | |
Chapter IV Vector Fields on a Manifold | 106 |
Chapter V Tensors and Tensor Fields on Manifolds | 176 |
Chapter VI Integration on Manifolds | 229 |
Chapter VII Differentiation on Riemannian Manifolds | 297 |
Chapter VIII Curvature | 365 |
References | 417 |
Index | 423 |
多く使われている語句
algebra basis bi-invariant C*-vector field compact completes the proof components connected coordinate frames coordinate neighborhood Corollary corresponding countable covariant tensor covering curve p(t defined definition denote derivative diffeomorphism differentiable manifold dimension domain of integration element equations equivalent Euclidean space example Exercise exists fact finite fixed point formula functions geodesic geometry given Gl(n hence homeomorphism homotopy identity imbedding inner product integral curve isometry isomorphism Lemma Let F Lie group G linear map mapping F matrix notation obtain one-parameter subgroup one-to-one open set open subset oriented orthogonal orthonormal parameter plane properly discontinuously properties prove rank real numbers regular submanifold Remark Riemannian manifold Riemannian metric Section Show structure submanifold subspace suppose surface symmetric tangent space tangent vector tensor field Theorem Let topology uniquely determined vector field vector space zero