On Infinitesimal Projective Transformations of the Tangent Bendle With the Complete Lift of A Finsler Metric

Behroz Bidabad, Morteza MirMorhamad Rezaii, Mosayeb Zohrehvand

Abstract


Let (M,g) be a Finsler manifold and TM0 its slit tangent bundle with the complete lift metric ~g.

In this paper we prove that every infinitesimal complete lift projective transformation on (TM0,~g), is an infinitesimal affine transformation. Moreover, if (M,g) is a Landsberg manifold, then there is a one-to-one correspondence between infinitesimal complete lift projective transformations on (TM0,~g) and infinitesimal affine transformations on (M,g).


Keywords


Finsler manifold‎, ‎Complete lift metric‎, ‎Tangent bundle‎, ‎Infinitesimal projective transformation.

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DOI: https://doi.org/10.22342/jims.23.1.397.1-12

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Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
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p-ISSN: 2086-8952 | e-ISSN: 2460-0245


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