万灵丹
发表于 2025-3-25 07:21:47
Harmonic Functionals and Related Topics,.) be an arbitrary chart of an arbitrary (pseudo-)Riemannian space ., let ||..|| be the matrix of components of the metric tensor . in the chart (.), and let . be its determinant. The transformation formula for the matrix of a quadratic form under a change of basis directly implies that under a chan
transplantation
发表于 2025-3-25 08:04:45
Gaussian Curvature,..., ..). Then the formula.defines the function <.> on ., which does not depend on the choice of the coordinates ..,..., ... Therefore, this formula correctly defines the function <.> on the whole manifold .
entitle
发表于 2025-3-25 13:50:20
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撕裂皮肉
发表于 2025-3-25 17:45:42
Einführung in den Wärme- und StoffaustauschProposition 3.2 implies that for any point p ∈ . of a locally symmetric connection space . there exists at most one affine mapping . → . that coincides with a locally geodesic symmetry .. on a certain normal neighborhood of the point .. This mapping (when it exists) is called a . and is denoted by .., as before.
不规则
发表于 2025-3-25 20:41:48
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cartilage
发表于 2025-3-26 00:18:43
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未完成
发表于 2025-3-26 07:00:01
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他一致
发表于 2025-3-26 12:29:48
Methoden der chinesischen Medizin,For a Riemannian (but not a pseudo-Riemannian) space . along with the energy Lagrangian, we can also consider the Lagrangian. which is expressed in local coordinates by
indoctrinate
发表于 2025-3-26 13:35:56
https://doi.org/10.1007/978-3-642-53260-3We can replace the real coordinates . and . on a surface . with one complex coordinate . = . + .. In the case where the coordinates . and . are isothermal, the coordinate . is called a . on the surface. (Certain authors also apply this name to the coordinates . and ..)
混沌
发表于 2025-3-26 19:10:27
Schallempfang und Schallaufzeichnung,For a (pseudo-)Riemannian space . we can use the metric tensor . to lower the superscript of the curvature tensor ., i.e., introduce a tensor of type (4,0) with the components . We emphasize that the lowered subscript is assumed to be the .. Specifically for this reason, the components of the tensor . are denoted by ...