SPHERES AND CIRCLES WITH RESPECT TO AN INDEFINITE METRIC ON A RIEMANNIAN MANIFOLD WITH A SKEW-CIRCULANT STRUCTURE

Georgi Dzhelepov, Iva Dokuzova, Dimitar Razpopov

DOI Number
https://doi.org/10.22190/FUMI220707044D
First page
683
Last page
695

Abstract


We study hyper-spheres, spheres and circles, with respect to an indefinite metric, in a single tangent space on a 4-dimensional differentiable manifold. The manifold is equipped with a positive definite metric and an additional tensor structure of type (1, 1). The fourth power of the additional structure is minus identity and its components form a skew-circulant matrix in some local coordinate system. The both structures are compatible and they determine an associated indefinite metric on the manifold.

Keywords

indefinite metric, tangent space, tensor structure, manifold.

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References


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DOI: https://doi.org/10.22190/FUMI220707044D

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