Department Of Mathematics And Statistics

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Author: search.filters.author.Shanker, G.

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    On the flag curvature of a homogeneous Finsler space with generalized m-Kropina metric
    (Balkan Society of Geometers, 2022-03-01T00:00:00) Kaur, J.; Shanker, G.; Jangir, S.
    In this paper, first, we give an explicit formula for the flag curvature of a homogeneous Finsler space with generalized m-Kropina metric. Then, we show that, under a mild condition, the two definitions of naturally reductive homogeneous Finsler space are equivalent for aforesaid metric. Finally, we study the flag curvature of naturally reductive homogeneous Finsler spaces with generalized m-Kropina metric. � Balkan Society of Geometers, Geometry Balkan Press 2022.
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    On CW-translations of homogeneous Finsler spaces with (?,?)-metrics
    (Balkan Society of Geometers, 2021-03-01T00:00:00) Rani, S.; Shanker, G.
    In the present paper, we consider homogeneous Finsler spaces with two (?,?)-metrics. Taking a Killing vector ?eld X on one of these spaces, we find necessary and su?cient conditions for X to be Killing on the other space. Further, by taking a Killing vector ?eld X of constant length on one of these spaces, we ?nd the condition under which the Killing vector ?led X has constant length w.r.t. other space also. Taking Killing vector ?elds of constant length, we ?nd CW translations on these spaces. � 2021 Balkan Society of Geometers, Geometry Balkan Press. All Rights Reserved.
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    On the rigidity of spherically symmetric Finsler metrics with isotropic E-curvature
    (Balkan Society of Geometers, 2021-01-01T00:00:00) Rani, S.; Shanker, G.
    In the current paper, first we establish the formula for mean Berwald curvature of a spherically symmetric Finsler metric. Further, we establish differential equations characterizing projectively flat as well as dually flat spherically symmetric Finsler metrics. Finally, we obtain a rigidity result on spherically symmetric Finsler metrics with isotropic E-curvature. � Balkan Society of Geometers, Geometry Balkan Press 2021.
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    On Kropina-Randers change of mth-root Finsler metric
    (Pushpa Publishing House, 2017) Shanker, G.; Baby, S.A.
    In the present paper, we consider the Kropina-Randers change of mth root Finsler metric. Firstly, we find the fundamental metric tensors of the Kropina-Randers transformed mth root Finsler metric, and then the necessary and sufficient condition under which the Kropina-Randers change of the mth root Finsler metric is locally dually flat. Further, we prove that the Kropina-Randers change of mth root Finsler metric is locally projectively flat if and only if it is locally Minkowskian. ? 2017 Pushpa Publishing House, Allahabad, India.
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    Four-dimensional conformally flat Berwald and Landsberg spaces
    (Informatics Publishing Limited and The Indian Mathematical Society, 2018) Shanker, G.
    The problem of conformal transformation and conformal atness of Finsler spaces has been studied in [6], [16], [17], [20], [21]. Recently, Prasad et. al [19] have studied three dimensional conformally at Landsberg and Berwald spaces and have obtained some important results. The purpose of the present paper is to extend the idea of conformal change to four dimensional Finsler spaces and find the suitable conditions under which a four dimensional conformally at Landsberg space becomes a Berwald space. ? 2018 Indian Mathematical Society.