Geodesics of Sasakian Metrics on Tensor Bundles |
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Authors: | Arif A Salimov Aydin Gezer Kursat Akbulut |
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Institution: | (1) Faculty of Science and Arts, Department of Mathematics, Ataturk University, 25240 Erzurum, Turkey |
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Abstract: | On the basis of the phase completion the notion of vertical and horizontal lifts of vector fields is defined in the tensor
bundles over a Riemannian manifold. Such a tensor bundle is made into a manifold with a Riemannian structure of special type
by endowing it with Sasakian metric. The components of the Levi-Civita and other metric connections with respect to Sasakian
metrics on tensor bundles with respect to the adapted frame are presented. This having been done, it is shown that it is possible
to study geodesics of Sasakian metrics dealing with geodesics of the base manifolds.
Dedicated to the memory of Vladimir Vishnevskii (1929-2007) |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 53C22 Secondary 53C25 |
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