A Frankel type theorem for CR submanifolds of Sasakian manifolds

Dario Di Pinto; Antonio Lotta

Archivum Mathematicum (2023)

  • Volume: 059, Issue: 5, page 369-381
  • ISSN: 0044-8753

Abstract

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We prove a Frankel type theorem for C R submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about C R submanifolds of Sasakian space forms.

How to cite

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Di Pinto, Dario, and Lotta, Antonio. "A Frankel type theorem for CR submanifolds of Sasakian manifolds." Archivum Mathematicum 059.5 (2023): 369-381. <http://eudml.org/doc/299133>.

@article{DiPinto2023,
abstract = {We prove a Frankel type theorem for $CR$ submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about $CR$ submanifolds of Sasakian space forms.},
author = {Di Pinto, Dario, Lotta, Antonio},
journal = {Archivum Mathematicum},
keywords = {intersection of submanifolds; CR submanifold of a Sasakian manifold; scalar Levi form},
language = {eng},
number = {5},
pages = {369-381},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A Frankel type theorem for CR submanifolds of Sasakian manifolds},
url = {http://eudml.org/doc/299133},
volume = {059},
year = {2023},
}

TY - JOUR
AU - Di Pinto, Dario
AU - Lotta, Antonio
TI - A Frankel type theorem for CR submanifolds of Sasakian manifolds
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 5
SP - 369
EP - 381
AB - We prove a Frankel type theorem for $CR$ submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about $CR$ submanifolds of Sasakian space forms.
LA - eng
KW - intersection of submanifolds; CR submanifold of a Sasakian manifold; scalar Levi form
UR - http://eudml.org/doc/299133
ER -

References

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  1. Bejancu, A., Geometry of CR-submanifolds, Mathematics and its Applications (East European Series), vol. 23, D. Reidel Publishing Co., Dordrecht, 1986. (1986) Zbl0605.53001MR0861408
  2. Bejancu, A., Papaghiuc, N., Semi-invariant submanifolds of a Sasakian manifold, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 27 (1981), 163–170. (1981) MR0618723
  3. Binh, T.Q., Ornea, L., Tamássy, L., Intersections of Riemannian submanifolds. Variations on a theme by T.J. Frankel, Rend. Mat. Appl. (7) 19 (1999), 107–121. (1999) MR1710117
  4. Blair, D.E., Riemannian Geometry of Contact and Symplectic Manifolds, second ed., Progress in Mathematics, vol. 203, Birkhäuser, Boston, 2010. (2010) Zbl1246.53001MR2682326
  5. Djorić, M., Okumura, M., 10.1007/978-1-4419-0434-8_16, Developments in Mathematics, vol. 19, Springer, New York, 2010. (2010) MR2566776DOI10.1007/978-1-4419-0434-8_16
  6. Falcitelli, M., Ianus, S., Pastore, A.M., Riemannian submersions and related topics, World Scientific Publishing Co., Singapore, 2004. (2004) MR2110043
  7. Frankel, T., 10.2140/pjm.1961.11.165, Pacific J. Math. 11 (1961), 165–171. (1961) MR0123272DOI10.2140/pjm.1961.11.165
  8. Goldberg, S.I., Kobayashi, S., 10.4310/jdg/1214428090, J. Differential Geom. 1 (1967), 225–233. (1967) MR0227901DOI10.4310/jdg/1214428090
  9. Medori, C., Nacinovich, M., 10.1023/A:1000166119593, Compositio Math. 109 (1997), 195–250. (1997) MR1478818DOI10.1023/A:1000166119593
  10. Pitis, G., 10.7146/math.scand.a-14415, Math. Scand. 93 (2003), 99–108. (2003) MR1997875DOI10.7146/math.scand.a-14415
  11. Sakai, T., Riemannian Geometry, Translations of Mathematical Monographs, vol. 149, Amer. Math. Soc., Providence, 1996. (1996) MR1390760
  12. Takahashi, T., 10.2748/tmj/1178240699, Tôhoku Math. J. 29 (1977), 91–113. (1977) MR0440472DOI10.2748/tmj/1178240699
  13. Tanno, S., Baik, S.-B., 10.2748/tmj/1178242811, Tôhoku Math. J. 22 (1970), 184–190. (1970) MR0268829DOI10.2748/tmj/1178242811
  14. Yano, K., Kon, M., 10.2996/kmj/1138036191, Kodai Math. J. 3 (1980), 163–196. (1980) MR0588453DOI10.2996/kmj/1138036191
  15. Yano, K., Kon, M., CR submanifolds of Kaehlerian and Sasakian manifolds, Progress in Mathematics, vol. 30, Birkhäuser, Boston, Mass., 1983. (1983) MR0688816
  16. Yano, K., Kon, M., Structures on Manifolds, Series in Pure Mathematics, vol. 3, World Scientific Publishing Co., Singapore, 1984. (1984) Zbl0557.53001MR0794310

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