×

Pseudo parallel CR-submanifolds in a non-flat complex space form. (English) Zbl 1357.53057

Summary: We classify pseudo parallel proper CR-submanifolds in a non-flat complex space form with CR-dimension greater than one. With this result, the non-existence of recurrent as well as semi parallel proper CR-submanifolds in a non-flat complex space form with CR-dimension greater than one can also be obtained.

MSC:

53C40 Global submanifolds
32V40 Real submanifolds in complex manifolds

References:

[1] A. C. Asperti, G. A. Lobos and F. Mercuri, Pseudo-parallel immersions in space forms, Mat. Contemp., 17 (1999), 59-70. · Zbl 0976.53019
[2] A. C. Asperti, G. A. Lobos and F. Mercuri, Pseudo-parallel submanifolds of a space form, Adv. Geom., 2 (2002), 57-71. · Zbl 1030.53058
[3] J. Berndt, S. Console and C. Olmos, Submanifolds and holonomy, Research Notes in Mathematics Series Vol. 434. Chapman & Hall/CRC, Boca Raton, 2003. · Zbl 1043.53044
[4] A. Bejancu, CR-submanifolds of a Kaehler manifold I, Proc. Amer. Math. Soc., 69 (1978), 135-142. · Zbl 0368.53040
[5] B. Y. Chen, CR-submanifolds of a Kaehler manifold, I, II, J. Diff. Geom., 16 (1981), 305-322; 16 (1981), 493-509.
[6] B. Y. Chen, Differential geometry of real submanifolds in a K”ahler manifold, Monatsh. 1562
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.