ON FINSLER MANIFOLDS WHOSE TANGENT BUNDLE HAS THE g-NATURAL METRIC
2011 ◽
Vol 08
(07)
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pp. 1593-1610
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Keyword(s):
In this paper, we introduce a Riemannian metric [Formula: see text] and a family of framed f-structures on the slit tangent bundle [Formula: see text] of a Finsler manifold Fn = (M, F). Then we prove that there exists an almost contact structure on the tangent bundle, when this structure is restricted to the Finslerian indicatrix. We show that this structure is Sasakian if and only if Fn is of positive constant curvature 1. Finally, we prove that (i) Fn is a locally flat Riemannian manifold if and only if [Formula: see text], (ii) the Jacobi operator [Formula: see text] is zero or commuting if and only if (M, F) have the zero flag curvature.
1978 ◽
Vol 82
(1-2)
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pp. 13-17
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1971 ◽
Vol 1971
(250)
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pp. 124-129
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1983 ◽
Vol 34
(1)
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pp. 1-6
Keyword(s):
2020 ◽
Vol 17
(08)
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pp. 2050122
Keyword(s):
Keyword(s):
2003 ◽
Vol 2003
(18)
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pp. 1155-1165
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1972 ◽
Vol 13
(4)
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pp. 447-450
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