Geometrical and physical characteristics of a class of conformal mappings

We consider conformal and concircular mappings of Eisenhart's generalized Riemannian spaces. We prove conformal and concircular invariance of some tensors in Eisenhart's generalized Riemannian spaces. We give new generalizations of symmetric spaces via Eisenhart's generalized Riemannian spaces. Finally, we describe some properties of covariant derivatives of tensors analogous to Yano's tensor of concircular curvature in Eisenhart symmetric spaces of various kinds.

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“…Obviously, the condition (3) is weaker than the condition (4) and it is independent of condition (5).…”

Section: Conformal Mappings Of Generalized Riemannian Spacesmentioning

confidence: 96%

“…A mapping between two generalized Riemannian spaces is said to be a conformal mapping if it preserves angles between curves of these spaces. Some physical characteristics of conformal mappings were given in [5]. Geodesic mappings and their generalizations is an active research field, see for instance [6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

On Conformal and Concircular Diffeomorphisms of Eisenhart’s Generalized Riemannian Spaces

2019

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“…Invariants of different geometrical mappings and their exact presentations are some of research subjects which results are used in different applications (for example, see [5]). Expressions of projective curvature tensors E k i jmn , Eq.…”

Section: Functionally Connected Projective Curvature Tensors and Paramentioning

confidence: 99%

Some properties of ET-projective tensors obtained from Weyl projective tensor

Stankovic

Zlatanović

Vesić

2015

Filomat

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Vanishing of linearly independent curvature tensors of a non-symmetric affine connection space as functions of vanished curvature tensor of the associated space of this one are analyzed in the first part of this paper. Projective curvature tensors of a non-symmetric affine connection space are expressed as functions of the affine connection coefficients and Weyl projective tensor of the corresponding associated affine connection space in the second part of this paper.

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“…In [10,17], a projective(projective-like) invariant of a quarter-symmetric metric connections was obtained. Afterwards, some properties of several types of a quarter-symmetric metric connection were studied ( [7,11,20,[23][24][25][27][28][29][30][31]). Recently, Han, Fu and Zhao [12,13] studied similar problems in Sub-Riemannian manifolds.…”

Section: Introductionmentioning

confidence: 99%

Geometries of manifolds equipped with a Ricci (projection-Ricci) quarter-symmetric connection

Tang

Chol

Tal

et al. 2019

Filomat

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We first introduce a Ricci quarter-symmetric connection and a projective Ricci quarter-symmetric connection, and then we investigate a Riemannian manifold admitting a Ricci (projective Ricci) quartersymmetric connection (M,), and prove that a Riamannian manifold with a Ricci(projection-Ricci) quartersymmetric connection is of a constant curvature manifold. Furthermore, we derive that an Einstein manifold (M,) is conformally flat under certain condition.

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Geometrical and physical characteristics of a class of conformal mappings

Cited by 26 publications

References 8 publications

On Conformal and Concircular Diffeomorphisms of Eisenhart’s Generalized Riemannian Spaces

On Conformal and Concircular Diffeomorphisms of Eisenhart’s Generalized Riemannian Spaces

Some properties of ET-projective tensors obtained from Weyl projective tensor

Geometries of manifolds equipped with a Ricci (projection-Ricci) quarter-symmetric connection

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