An Introduction to Differentiable Manifolds and Riemannian GeometryAcademic Press, 1986/04/21 - 429 ページ An Introduction to Differentiable Manifolds and Riemannian Geometry |
この書籍内から
検索結果1-5 / 63
5 ページ
... coordinate system, as we have seen. It then becomes difficult at times to distinguish underlying geometric properties from those which depend on the choice of coordinates. An example: Having identified E° and R* and lines with the ...
... coordinate system, as we have seen. It then becomes difficult at times to distinguish underlying geometric properties from those which depend on the choice of coordinates. An example: Having identified E° and R* and lines with the ...
10 ページ
... system of coordinates for the entire space, that is, to establish a correspondence between all of E" and R". Built ... coordinate neighborhood and the numbers x*(q), ..., x"(a), given by p(q) = (x'(q), ..., x"(q)), the coordinates of ...
... system of coordinates for the entire space, that is, to establish a correspondence between all of E" and R". Built ... coordinate neighborhood and the numbers x*(q), ..., x"(a), given by p(q) = (x'(q), ..., x"(q)), the coordinates of ...
31 ページ
... coordinate system, we see that x(0) is the ith component of the velocity vector of the particle whose motion is given by x(t) = (x'(t), ..., x"(t)) at the instant it passes through a (see Fig. II.3). Two curves are equivalent if they ...
... coordinate system, we see that x(0) is the ith component of the velocity vector of the particle whose motion is given by x(t) = (x'(t), ..., x"(t)) at the instant it passes through a (see Fig. II.3). Two curves are equivalent if they ...
55 ページ
... coordinate system, p e V C U, is (p) = (0,0,...,0), and p(V) = B(0) or Co(0). Using the theorem just proved, we give some preliminary examples of manifolds. (1.5) Example (The Euclidean plane) (See comments in Section I.2.) Once a unit ...
... coordinate system, p e V C U, is (p) = (0,0,...,0), and p(V) = B(0) or Co(0). Using the theorem just proved, we give some preliminary examples of manifolds. (1.5) Example (The Euclidean plane) (See comments in Section I.2.) Once a unit ...
56 ページ
... coordinate system. Again, this may be done in a variety of ways. As we have noted it is customary to identify E" and R" since the former is difficult to axiomatize; this is equivalent to choosing a fixed rectangular Cartesian coordinate ...
... coordinate system. Again, this may be done in a variety of ways. As we have noted it is customary to identify E" and R" since the former is difficult to axiomatize; this is equivalent to choosing a fixed rectangular Cartesian coordinate ...
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