Some results on the geometry of warped product CR-submanifolds in quasi-Sasakian manifold

• Autores: Shamsur Rahman
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 24, Nº. 1, 2022, págs. 105-114
• Idioma: inglés
• DOI: 10.4067/S0719-06462022000100105
• Enlaces
  • Texto completo
• Resumen
  • español

    RESUMEN El presente artículo trata de un estudio de subvariedades producto alabeadas de variedades cuasi-Sasakianas y CR subvariedades producto alabeadas de variedades cuasi-Sasakianas. Hemos mostrado que el producto alabeado de tipo M = D⊥×yDT no existe, donde D⊥ y DT son subvariedades invariantes y anti-invariantes de una ariedad cuasi-Sasakiana M, respectivamente. Más aún, hemos obtenido resultados de caracterización para que CR-subvariedades sean localmente CR-productos alabeados.

  • English

    ABSTRACT The present paper deals with a study of warped product submanifolds of quasi-Sasakian manifolds and warped product CR-submanifolds of quasi-Sasakian manifolds. We have shown that the warped product of the type M = D⊥×yDT does not exist, where D⊥ and DT are invariant and antiinvariant submanifolds of a quasi-Sasakian manifold M, respectively. Moreover we have obtained characterization results for CR-submanifolds to be locally CR-warped products.

• Referencias bibliográficas
  • Arslan, K.,Ezentas, R.,Mihai, I.,Murathan, C.. (2005). Contact CR-warped product submanifolds in Kenmotsu space forms. J. Korean Math. Soc.....
  • Bejancu, A.. (1978). CR-submanifold of a Kaehler manifold. I. Proc. Amer. Math. Soc.. 69. 135
  • Bejancu, A.,Papaghiuc, N.. (1981). Semi-invariant submanifolds of a Sasakian manifold.. An. Ştiinţ. Univ. “Al. I. Cuza” Iaşi Secţ. I a Mat.....
  • Binh, T.-Q.,De, A.. (2014). On contact CR-warped product submanifolds of a quasi-Sasakian manifold. Publ. Math. Debrecen. 84. 123
  • Bishop, R. L.,O’Neill, B.. (1969). Manifolds of negative curvature. Trans. Amer. Math. Soc.. 145. 1-49
  • Blair, D. E.. (1976). Contact manifolds in Riemannian geometry. Springer-Verlag. Berlin-New York.
  • Calin, C.. (1998). Contributions to geometry of CR-submanifold. University of Iaşi. Iaşi, Romania.
  • Che, B.-Y.. (2001). Geometry of warped product CR-submanifolds in Kaehler manifolds. Monatsh. Math.. 133. 177
  • Hasegawa, I.,Mihai, I.. (2003). Contact CR-warped product submanifolds in Sasakian manifolds. Geom. Dedicata. 102. 143
  • Hiepko, S.. (1979). Eine innere Kennzeichnung der verzerrten Produkte. Math. Ann.. 241. 209
  • Munteanu, M.-I.. (2007). A note on doubly warped product contact CR-submanifolds in trans-Sasakian manifolds. Acta Math. Hungar.. 116. 121
  • Yano, K.. (1963). On structure defined by a tensor field f of type (1, 1) satisfying f3+f = 0. Tensor. 14. 99-109
  • Yano, K.,Kon, M.. (1984). Structures on manifolds. World Scientific Publishing Co.. Singapore.