Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 19 (2024), 167 -- 178

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PROJECTIVELY FLAT CUBIC (α, β)-METRIC WITH CONSTANT FLAG CURVATURE K = 0

Brijesh Kumar Tripathi, Dhruvisha Patel and V. K. Chaubey

Abstract. Finsler metrics with straight geodesics on an open subset in Rn are thought to be projective. The flag curvature of any projective Finsler metric is known to be a scalar function of tangent vectors (the flag curvature must be a constant if it is Riemannian). We categorize locally projectively flat cubic (α, β)-metric with constant Ricci curvature and obtain cubic (α, β)-metric of zero flag curvature.

2020 Mathematics Subject Classification: 53B40, 53C60, 53A20, 53B10.
Keywords: Finsler space, Projective change, cubic (α, β)-metric, Projective flatness, Flag curvature.

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Brijesh Kumar Tripathi
Department of Mathematics, L.D. College of Engineering Ahmedabad,
Gujarat, 380015, India.
E-mail: *brijeshkumartripathi4@gmail.com


Dhruvisha Patel
Research Scholar, Science_Mathematics Branch,
Gujarat Technological University, Ahmedabad,
Gujarat, 382424, India.
E-mail: dhruvisha14299@gmail.com


V. K. Chaubey
Department of Mathematics, North-Eastern Hill University,
Shillong, 793022, Meghalaya, India.
E-mail: vkcoct@gmail.com


https://www.utgjiu.ro/math/sma