Geodesic
Spheres and circles in the tangent space at a point on a Riemannian manifold with respect to an indefinite metric
Novi Sad Journal of Mathematics, Tome 48 (2018) no. 1.

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We consider a 3-dimensional Riemannian manifold with an additional circulant structure, whose third power is the identity. This structure is compatible with the metric such that an isometry is induced in any tangent space of the manifold. Further, we consider an associated metric with the Riemannian metric, which is necessarily indefinite. We find equations of a sphere and equations of a circle, which are given with respect to the associated metric, in terms of the Riemannian metric.
Publié le :
DOI : 10.30755/NSJOM.07233
Classification : 53B30, 53B20, 15B05, 51N20
Keywords: Riemannian manifold, circulant matrix, indefinite metric tensor, sphere equation, time-like, space-like 
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     author = {Georgi Dzhelepov},
     title = {Spheres and circles in the tangent space at a point on a {Riemannian} manifold with respect to an indefinite metric},
     journal = {Novi Sad Journal of Mathematics},
     pages = {143 - 150},
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     year = {2018},
     doi = {10.30755/NSJOM.07233},
     url = {http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.07233/}
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Georgi Dzhelepov. Spheres and circles in the tangent space at a point on a Riemannian manifold with respect to an indefinite metric. Novi Sad Journal of Mathematics, Tome 48 (2018) no. 1. doi : 10.30755/NSJOM.07233. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.07233/

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