scholarly journals On projective-symmetric spaces

1964 ◽  
Vol 4 (1) ◽  
pp. 113-121 ◽  
Author(s):  
Bandana Gupta
Keyword(s):  
Symmetric Space ◽  
Curvature Tensor ◽  
Symmetric Spaces ◽  
Covariant Differentiation ◽  
Metric Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Image Position ◽  
Riemannian Spaces

This paper deals with a type of Remannian space Vn (n ≧ 2) for which the first covariant dervative of Weyl's projective curvature tensor is everywhere zero, that is where comma denotes covariant differentiation with respect to the metric tensor gij of Vn. Such a space has been called a projective-symmetric space by Gy. Soós [1]. We shall denote such an n-space by ψn. It will be proved in this paper that decomposable Projective-Symmetric spaces are symmetric in the sense of Cartan. In sections 3, 4 and 5 non-decomposable spaces of this kind will be considered in relation to other well-known classes of Riemannian spaces defined by curvature restrictions. In the last section the question of the existence of fields of concurrent directions in a ψ will be discussed.

scholarly journals On conformally recurrent spaces of second order

1969 ◽  
Vol 10 (1-2) ◽  
pp. 155-161 ◽  
Author(s):  
M. C. Chaki ◽  
A. N. Roy Chowdhury
Keyword(s):  
Curvature Tensor ◽  
Second Order ◽  
Covariant Differentiation ◽  
Metric Tensor ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Image Position ◽  
Conformally Recurrent ◽  
Zero Vector ◽  
Riemannian Spaces

In a recent paper [1] Adati and Miyazawa studied conformally recurrent spaces, that is, Riemannian spaces defined by where is the conformal curvature tensor: λi is a non-zero vector and comma denotes covariant differentiation with respect to the metric tensor gij.

scholarly journals Projective-symmetric spaces

1967 ◽  
Vol 7 (1) ◽  
pp. 48-54 ◽  
Author(s):  
R. F. Reynolds ◽  
A. H. Thompson
Keyword(s):  
Curvature Tensor ◽  
Covariant Derivative ◽  
Symmetric Spaces ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Riemannian Spaces

Gy. Soos [1] and B. Gupta [2] have discussed the properties of Riemannian spaces Vn (n > 2) in which the first covariant derivative of Weyl's projective curvature tensor is everywhere zero; such spaces they call Protective-Symmetric spaces. In this paper we wish to point out that all Riemannian spaces with this property are symmetric in the sense of Cartan [3]; that is the first covariant derivative of the Riemann curvature tensor of the space vanishes. Further sections are devoted to a discussion of projective-symmetric af fine spaces An with symmetric af fine connexion. Throughout, the geometrical quantities discussed will be as defined by Eisenhart [4] and [5].

scholarly journals Generalized Projectively Symmetric Spaces

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Dariush Latifi ◽  
Asadollah Razavi
Keyword(s):  
Curvature Tensor ◽  
Symmetric Spaces ◽  
Geometric Properties ◽  
Projective Curvature ◽  
Projective Curvature Tensor

We study generalized projectively symmetric spaces. We first study some geometric properties of projectively symmetric spaces and prove that any such space is projectively homogeneous and under certain conditions the projective curvature tensor vanishes. Then we prove that given any regular projective s-space (, ), there exists a projectively related connection , such that (, ) is an affine s-manifold.

A spacetime with pseudo-projective curvature tensor

2016 ◽  
Vol 57 (6) ◽  
pp. 062501 ◽  
Author(s):  
Sahanous Mallick ◽  
Young Jin Suh ◽  
Uday Chand De
Keyword(s):  
Curvature Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor

scholarly journals Vassiliev invariants from symmetric spaces

2016 ◽  
Vol 25 (10) ◽  
pp. 1650055 ◽  
Author(s):  
Indranil Biswas ◽  
Niels Leth Gammelgaard
Keyword(s):  
Symmetric Space ◽  
Lie Algebra ◽  
Curvature Tensor ◽  
Symmetric Spaces ◽  
Weight System ◽  
Riemannian Symmetric Space ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Vassiliev Invariants ◽  
Chord Diagrams

We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a tangent space. Among the Lie algebra weight systems, they are exactly characterized by having the symmetries of the Riemann curvature tensor.

scholarly journals ON THE $\mathcal{M}$--PROJECTIVE CURVATURE TENSOR OF A $(k, \mu)$-CONTACT METRIC MANIFOLD

2017 ◽  
pp. 117
Author(s):  
D. G. Prakasha ◽  
Kakasab Mirji
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Sasakian Manifold ◽  
Riemannian Curvature ◽  
Contact Metric Manifold ◽  
Contact Metric Manifolds ◽  
Riemannian Curvature Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor

The paper deals with the study of $\mathcal{M}$-projective curvature tensor on $(k, \mu)$-contact metric manifolds. We classify non-Sasakian $(k, \mu)$-contact metric manifold satisfying the conditions $R(\xi, X)\cdot \mathcal{M} = 0$ and $\mathcal{M}(\xi, X)\cdot S =0$, where $R$ and $S$ are the Riemannian curvature tensor and the Ricci tensor, respectively. Finally, we prove that a $(k, \mu)$-contact metric manifold with vanishing extended $\mathcal{M}$-projective curvature tensor $\mathcal{M}^{e}$ is a Sasakian manifold.

On an Upper Bound for the Heat Kernel on SU*(2n)/ Sp(n)

1994 ◽  
Vol 37 (3) ◽  
pp. 408-418 ◽  
Author(s):  
P. Sawyer
Keyword(s):  
Symmetric Space ◽  
Heat Kernel ◽  
Upper Bound ◽  
Symmetric Spaces ◽  
Legendre Function ◽  
Noncompact Type ◽  
Image Position

AbstractJean-Philippe Anker made an interesting conjecture in [2] about the growth of the heat kernel on symmetric spaces of noncompact type. For any symmetric space of noncompact type, we can writewhere ϕ0 is the Legendre function and q, "the dimension at infinity", is chosen such that limt—>∞Vt(x) = 1 for all x. Anker's conjecture can be stated as follows: there exists a constant C > 0 such thatwhere is the set of positive indivisible roots. The behaviour of the function ϕ0 is well known (see [1]).The main goal of this paper is to establish the conjecture for the spaces SU*(2n)/ Sp(n).

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