Geodesic Vector Fields on a Riemannian Manifold
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A unit geodesic vector field on a Riemannian manifold is a vector field whose integral curves are geodesics, or in other worlds have zero acceleration. A geodesic vector field on a Riemannian manifold is a smooth vector field with acceleration of each of its integral curves is proportional to velocity. In this paper, we show that the presence of a geodesic vector field on a Riemannian manifold influences its geometry. We find characterizations of n-spheres as well as Euclidean spaces using geodesic vector fields.
2018 ◽
Vol 148
(4)
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pp. 773-818
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2019 ◽
Vol 13
(06)
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pp. 2050120
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2021 ◽
Vol 62
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pp. 53-66
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2019 ◽
Vol 30
(4)
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pp. 542-552
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2014 ◽
Vol 24
(07)
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pp. 1450090
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2014 ◽
Vol 25
(11)
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pp. 1450104
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