IKBFU's Vestnik

2013 Issue №10

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Covariant differentials and covariant derivatives associated with surface of projective space

Pages
60-63

Abstract

The paper is concerned with m-dimensional surface in n-dimensional projective space. In studying fundamental-group connection Bianchi identities are found. It is proved that alternated covariant derivatives for the components of the first type connection object are equal to the corresponding components of the curvature tensor, and the ones of the third type vanish.

Reference

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2. Шевченко Ю. И. Оснащения центропроективных многообразий. Калининград, 2000.
3. Polyakova K. V. Parallel displacements on the surface of a projective space // Journal of Mathematical Sciences. 2009. Vol. 162, No. 5. P. 675—709.