Olszak, Zbigniew (1994) On totally geodesic affine immersions into affine manifolds of recurrent projective curvature. Accademia Peloritana dei Pericolanti, Classe di Scienze FF. MM. NN., LXXII. pp. 361-373.
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Abstract
In the previous paper [8], the author has studied totally geodesic affine immersions $f:(M, \nabla \ ) \to \ ( \bar M \, \bar \nabla \ ) $ in the case when $( \bar M \, \bar \nabla \ ) $ is an affine manifold of recurrent curvature. It is shown there that $(M, \nabla \ ) $ is flat or of recurrent curvature. And if $f$ is additionally umbilical with non-zero shape tensor and dim $M \ge \ 3$, then $(M, \nabla \ ) $ is locally projectively flat.
In the presented paper, the investigation of totally geodesic affine immersions is continued. We assume that the ambient manifold $( \bar M \ , \bar \nabla \ ) $ is of recurrent projective curvature. It is proved that if dim $M \ge \ 3$, then $(M, \nabla \ ) $ is locally projectively flat or of recurrent projective curvature. Moreover, if $f$ is additionally umbilical with non-zero shape tensor, then $(M, \nabla \ ) $ is locally projectivvely flat.
| Item Type: | Article |
|---|---|
| Subjects: | M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali > 1994 M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Medico-Biologiche > 1994 M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Giuridiche, Economiche e Politiche > 1994 M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Lettere Filosofia e belle Arti > 1994 |
| Depositing User: | Dr A F |
| Date Deposited: | 19 Sep 2012 11:42 |
| Last Modified: | 19 Sep 2012 11:43 |
| URI: | http://cab.unime.it/mus/id/eprint/694 |
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