Topic
Ricci decomposition
About: Ricci decomposition is a research topic. Over the lifetime, 1972 publications have been published within this topic receiving 45295 citations.
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TL;DR: In this paper, an expansion for the Weil-Petersson Riemann curvature tensor in the thin region of the Teichm-u-ller and moduli spaces was developed for disjoint geodesics.
Abstract: An expansion is developed for the Weil-Petersson Riemann curvature tensor in the thin region of the Teichm\"{u}ller and moduli spaces. The tensor is evaluated on the gradients of geodesic-lengths for disjoint geodesics. A precise lower bound for sectional curvature in terms of the surface systole is presented. The curvature tensor expansion is applied to establish continuity properties at the frontier strata of the augmented Teichm\"{u}ller space. The curvature tensor has the asymptotic product structure already observed for the metric and covariant derivative. The product structure is combined with the earlier negative sectional curvature results to establish a classification of asymptotic flats. Furthermore, tangent subspaces of more than half the dimension of Teichm\"{u}ller space contain sections with a definite amount of negative curvature. Proofs combine estimates for uniformization group exponential-distance sums and potential theory bounds.
21 citations
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TL;DR: In this paper, the authors studied the tensor product of two Euclidean plane curves and established necessary and sufficient conditions for such a product to be totally real or complex or slant.
Abstract: Recently B.Y. CHEN initiated the study of the tensor product immersion of two immersions of a given Riemannian manifold [3]. In [6] the particular case of tensor product of two Euclidean plane curves was studied. The minimal one were classified, and necessary and sufficient conditions for such a tensor product to be totally real or complex or slant were established. In the present paper we study for tensor product of Euclidean plane curves the problem of B.Y. CHEN: to what extent do the properties of the tensor product immersion f ⊗ h of two immersions f, h determines the immersions f, h ? [3]
21 citations
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31 Jan 2001
TL;DR: In this paper, a quasi-simple group of Lie type deened over a group of characteristic p is determined whether it can possess irreducible Brauer characters in characteristic other than p.
Abstract: Let G be a nite quasi-simple group of Lie type deened over a eld of characteristic p. We determine whether G can possess irreducible Brauer characters , (of degree > 1) in characteristic other than p such that is irreducible.
21 citations
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TL;DR: This work surveys the theory of discrete surface Ricci flow, its computational algorithms, and the applications for surface registration and shape analysis.
Abstract: Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a nonlinear heat diffusion process, and becomes constant eventually. Ricci flow is a powerful computational tool to design Riemannian metrics by prescribed curvatures. Surface Ricci flow has been generalized to the discrete setting. This work surveys the theory of discrete surface Ricci flow, its computational algorithms, and the applications for surface registration and shape analysis.
21 citations
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TL;DR: In this paper, generalized Sasakian-space-forms with vanishing quasi-conformal curvature tensor were studied. And the space-forms satisfying ▿S = 0 and R.S = 1 were considered.
Abstract: The object of the present paper is to study generalized Sasakian-space-forms with vanishing quasi-conformal curvature tensor. The space-forms satisfying ▿S = 0 and R.S = 0 are also considered.
21 citations