On contact screen conformal null submanifolds
Resumen
First, we prove that indefinite Sasakian manifolds do not admit any screen conformal $r$-null submanifolds, tangent to the structure vector field. We, therefore, define a special class of null submanifolds, called; {\it contact screen conformal} $r$-null submanifold of indefinite Sasakian manifolds. Several characterization results, on the above class of null submanifolds, are proved. In particular, we prove that such null submanifolds exist in indefinite Sasakian space forms of constant holomorphic sectional curvatures of $-3$.
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C. Atindogbe, Scalar curvature on lightlike hypersurfaces, Balkan Society of Geometers, Geometry Balkan Press 2009, Applied Sciences, 11, 9-18, (2009).
C. Calin, Contributions to geometry of CR-submanifold, Ph.D. Thesis, University of Iasi (Romania), (1998).
J. Dong and X. Liu, Totally Umbilical Lightlike Hypersurfaces in Robertson-Walker Spacetimes, Hindawi Publishing Corporation, Volume 2014, Article ID 974695, 10 pages. DOI: https://doi.org/10.1155/2014/974695
K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Mathematics and Its Applications, Kluwer Academic Publishers, (1996). DOI: https://doi.org/10.1007/978-94-017-2089-2
K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, Birkhauser Verlag, Basel, (2010). DOI: https://doi.org/10.1007/978-3-0346-0251-8
K. L. Duggal and B. Sahin, Screen conformal half lightlike submanifolds, Int. J. Math. Math. Sci., 68, 3737-3753, (2004). DOI: https://doi.org/10.1155/S0161171204403342
K. L. Duggal and D. H. Jin, Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, (2007). DOI: https://doi.org/10.1142/6449
K. L. Duggal and A. Bejancu, Lightlike CR hypersurfaces of indefinite Kaehler manifolds, Acta Applicandae Mathematicae, 31, 171-190, (1993). DOI: https://doi.org/10.1007/BF00990541
D. H. Jin, Ascreen lightlike hypersurfaces of an indefinite Sasakian manifold. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math., 20(1), 25-35, (2013). DOI: https://doi.org/10.7468/jksmeb.2013.20.1.25
D. H. Jin, Geometry of lightlike hypersurfaces of an indefinite sasakian manifold, Indian J. Pure Appl. Math., 41(4), 569-581, (2010). DOI: https://doi.org/10.1007/s13226-010-0032-y
D. H. Jin, Special lightlike hypersurfaces of indefinite Kaehler manifolds, Filomat, 30(7), 1919-1930, (2016). DOI: https://doi.org/10.2298/FIL1607919J
F. Massamba and S. Ssekajja, Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds, Arab. J. Math., 5, 87-101, (2016). DOI: https://doi.org/10.1007/s40065-016-0146-0
D. N. Kupeli, Singular semi-Riemannian geometry, Mathematics and Its Applications, Vol. 366, Kluwer Academic Publishers, (1996). DOI: https://doi.org/10.1007/978-94-015-8761-7
A. Upadhyay, R. S. Gupta and A. Sharfuddin, Screen conformal lightlike hypersurfaces of an indefinite cosymplectic manifold, Georgian Mathematical Journal, 24(4), 609-620, (2017). DOI: https://doi.org/10.1515/gmj-2016-0044
Derechos de autor 2022 Boletim da Sociedade Paranaense de Matemática
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