Spheres and circles with respect to an indefinite metric on a Riemanian manifold with a skew-circulant structure

Georgi Dzhelepov; Iva Dokuzova; Dimitar Razpopov

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arXiv · 2301.03675

Spheres and circles with respect to an indefinite metric on a Riemanian manifold with a skew-circulant structure

Georgi Dzhelepov·Iva Dokuzova·Dimitar Razpopov

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Abstract

We study hyper-spheres, spheres and circles, with respect to an indefinite metric, in a 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)11. 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.

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Georgi Dzhelepov, Iva Dokuzova, Dimitar Razpopov. 2023-01-09. Spheres and circles with respect to an indefinite metric on a Riemanian manifold with a skew-circulant structure. https://arxiv.org/abs/2301.03675

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