Connections with parallel skew-symmetric torsion on sub-Riemannian manifolds
On a sub-Riemannian manifold M of contact type, is considered an N-connection defined by the pair (, N), where is an interior metric connection, is an endomorphism of the distribution D. It is proved that there exists a unique N-connection such that its torsion is skew-symmetric as a contravariant t...
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| Format: | Article |
| Language: | English |
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Immanuel Kant Baltic Federal University
2020-08-01
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| Series: | Дифференциальная геометрия многообразий фигур |
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| Online Access: | https://journals.kantiana.ru/geometry/4686/25778/ |
| Summary: | On a sub-Riemannian manifold M of contact type, is considered an N-connection defined by the pair (, N), where is an interior metric connection, is an endomorphism of the distribution D. It is proved that there exists a unique N-connection such that its torsion is skew-symmetric as a contravariant tensor field. A construction of the endomorphism corresponding to such connection is found. The sufficient conditions for the obtained connection to be a metric connection with parallel torsion are given.
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| ISSN: | 0321-4796 2782-3229 |