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The geometry of Finsler spaces of \(H_p\)-scalar curvature. (English) Zbl 1446.53060

Summary: The aim of the present paper is to provide an intrinsic investigation of special Finsler spaces of \(H_p\)-scalar curvature and of \(H_p\)-constant curvature. Characterizations of such spaces are given. A sufficient condition for Finsler space of \(H_p\)-scalar curvature to be of perpendicular scalar curvature is investigated. Necessary and sufficient conditions under which a Finsler space of scalar curvature turns into a Finsler space of \(H_p\)-scalar curvature are shown. Further, certain conditions under which a Finsler manifolds of \(H_p\)-scalar curvature and of scalar curvature reduce to a Finsler space of \(H_p\)-constant curvature are obtained. Finally, various examples are studied and constructed.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)

Software:

Finsler
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Full Text: arXiv Link

References:

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