冷峻
发表于 2025-3-28 17:50:00
Curvature in Riemannian Space,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 ...
nostrum
发表于 2025-3-28 19:02:30
Some Special Tensors,The Gauss—Bonnet theorem in the previous chapter directly implies that the ... (it is the same for all metrics).
一窝小鸟
发表于 2025-3-29 00:59:14
Surfaces with Conformal Structure,The curvature tensor . of a (pseudo-)Riemannian space χ according to Corollary 17.1, admits a decomposition of the form . where . is the Bianchi tensor with the components . the .. The latter tensor has an interesting geometric sense.
猛烈责骂
发表于 2025-3-29 06:49:59
Mappings and Submanifolds I,Let . and . be Riemannian (or pseudo-Riemannian) spaces with the metric tensors . and . and the Riemannian connections ∇. and ∇.. Moreover, let . = dim . and . = dim ..
引水渠
发表于 2025-3-29 10:30:13
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Badger
发表于 2025-3-29 15:03:35
Geometry VI978-3-662-04433-9Series ISSN 0938-0396
得罪
发表于 2025-3-29 15:49:37
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groggy
发表于 2025-3-29 19:57:05
Einführung in den Sprachkern von SQL-99= (., .., ...,..) of the manifold . defines a chart (.., ..) of the manifold .. for which .. = .... The coordinates of the vector . ∈ .. in this chart are the coordinates .., ..., .. of the point . = .. in the chart (.) and the coordinates of this vector in the basis . of the linear space .... The l
非秘密
发表于 2025-3-30 02:28:58
Reiner Kolla,Paul Molitor,Hans Georg Osthofwith respect to an arbitrary connection ∇ on a manifold . are operators.defined on the linear space α. and having properties 1, 2, and 3 indicated in Chap. 1. Moreover, because for ξ = .., the vector bundle T.. ξ is just the tensor bundle .... over the manifold ., in accordance with the general resu
Hemiplegia
发表于 2025-3-30 05:35:24
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