On the linear Weingarten spacelike submanifolds immersed in a locally symmetric semi-Riemannian space

Araújo, Jogli G.; Barboza, Weiller F. C.; Lima, Henrique F. de; Velásquez, Marco Antonio L.

doi:10.1007/s13366-019-00469-4

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2020

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“…This type of metrics was first studied by Arthur Geoffrey Walker in 1950. Any Walker metric can be written to the standard form using a suitable local coordinate [7].…”

Section: Introductionmentioning

confidence: 99%

Symmetric Spaces in Riemannian and Semi-Riemannian Geometry

Hashempour

Seyedvalilo²

2020

ARJOM

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In this paper, we will obtain the necessary and sufficient conditions for the analysis of the position of local symmetry on an arbitrary Riemannian manifold. These conditions are devoid of the aspects of Lie groups, and thus can be used in calculations of procedures, without interfering with the concepts of Lie groups, and improve intuitive attitudes. Also, we will study and create equivalent conditions for a situation where a two-metric homogeneous Riemannian manifold is located symmetrically. In addition, in this paper it is stated that the symmetric space (M, g) can be seen as a homogeneous space G/K. Also, one-to-one correspondence between the symmetric space and the symmetric pair is shown, and curvature is studied on a symmetric space.

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“…This type of metrics was first studied by Arthur Geoffrey Walker in 1950. Any Walker metric can be written to the standard form using a suitable local coordinate [7].…”

Section: Introductionmentioning

confidence: 99%

Symmetric Spaces in Riemannian and Semi-Riemannian Geometry

Hashempour

Seyedvalilo²

2020

ARJOM

View full text Add to dashboard Cite

show abstract

On the linear Weingarten spacelike submanifolds immersed in a locally symmetric semi-Riemannian space

Cited by 1 publication

References 14 publications

Symmetric Spaces in Riemannian and Semi-Riemannian Geometry

Symmetric Spaces in Riemannian and Semi-Riemannian Geometry

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