TY - JOUR T1 - A STUDY ON GCR-LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS AU - Poyraz, Nergiz PY - 2021 DA - January Y2 - 2021 DO - 10.33773/jum.876269 JF - Journal of Universal Mathematics JO - JUM PB - Gökhan ÇUVALCIOĞLU WT - DergiPark SN - 2618-5660 SP - 25 EP - 33 VL - 4 IS - 1 LA - en AB - We study GCR-lightlike submanifolds of semi-Riemannian product manifolds. We give some equivalent conditions for the integrability of various distributions of GCR-lightlike submanifolds of semi-Riemannian product manifolds and investigate the geometry of leaves of distributions. KW - Semi-Riemannian product manifolds KW - Lightlike submanifolds KW - GCR-lightlike submanifolds CR - Atçeken, M. and Kılıç, E. Semi-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifol, Kodai Math. J. Vol. 30, No. 3, (2007), pp. 361-378 CR - Doğan, B., ¸Sahin, B., & Yaşar, E. (2019). Screen Generic Lightlike Submanifolds. Mediterranean Journal of Mathematics, 16(4), 104. CR - Duggal, K. L., Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Academic Publishers, Dordrecht (1996) CR - Duggal, K. L., Şahin B.: Screen Cauchy Riemann lightlike submanifolds. Acta Math. Hung. 106(1-2), 125–153 (2005) CR - Duggal, K. L., Şahin B.: Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds. Acta Math. Hung. 112(1-2), 107-130 (2006) CR - Duggal, K. L., Şahin, B.: Generalized Cauchy-Riemann lightlike submanifolds of indefinite Sasakian manifolds. Acta Math. Hung. 122(1-2), 45-58 (2009) CR - Duggal, K. L., Şahin B.: Di¤erential Geometry of Lightlike Submanifolds. Birkhäuser, Basel (2010) CR - Gupta, R.S., Sharfuddin, A.: Generalised Cauchy-Riemann lightlike submanifolds of indefinite Kenmotsu manifolds. Note di Matematica 30(2), 49-60 (2011). CR - Gupta, R.S., Upadhyay, A., Sharfuddin, A.: Generalised Cauchy-Riemann lightlike submanifolds of inde…nite cosymplectic manifolds. An. ¸Stiin¸t. Univ. Al. I. CuzaIa¸si. Mat. (N.S.), 58(2), 381-394 (2012). CR - Khursheed Haider S. M., Thakur, M. and Advin, Screen Cauchy-Riemann lightlike submanifolds of a semi-Riemannian product manifold, Int. Electron. J. Geom. 4, no. 2, 141-155, (2011) CR - Kılıç, E., & Şahin, B. Radical Anti-Invariant Lightlike Submanifolds of Semi-Riemannian Product Manifolds. Turkish Journal of Mathematics, 32(4), 429-449,(2008). CR - Kılıç, E., Şahin, B. and Keleş, S., Screen semi-invariant lightlike submanifolds of a semi-Riemannian product manifolds, Int. Electron. J. Geom. 4 , 120-135, (2011). CR - Kumar, R., Jain, V., Nagaich, R. K., GCR-lightlike product of inde…nite Sasakian manifolds. Advances in Mathematical Physics, 2011, Article ID 983069, 1-13 (2011) CR - Kumar, R., Kumar, S., & Nagaich, R. K. Integrability of distributions in GCR-lightlike submanifolds of inde…nite Kaehler manifolds. Communications of the Korean Mathematical Society, 27(3), 591-602, (2012). CR - Kumar, S., Kumar, R., Nagaich, R. K.: GCR-lightlike submanifolds of a semi-Riemannian product manifold. Bull. Korean Math. Soc. 51(3), 883-899 (2014) CR - D. N. Kupeli, Singular Semi-Riemannian Geometry, vol. 366, Kluwer, Dordrecht, 1996. CR - Perkta¸s, S. Y., Kılıç, E., Keleş, S., Warped product submanifolds of Lorentzian paracosymplectic manifolds. Arabian Journal of Mathematics, 1(3), 377-393, (2012). CR - Poyraz, N. Ö. Golden GCR-Lightlike Submanifolds of Golden Semi-Riemannian Manifolds. Mediterranean Journal of Mathematics, 17(5), 1-16 (2020). CR - Senlin, X. and Yilong, N., Submanifolds of Product Riemannian Manifold. Acta Mathematica Scientia, 20(B), 213-218, (2000). CR - Şahin, B. Lightlike submanifolds of indefinite quaternion Kaehler manifolds. Demonstratio Mathematica, 40(3), 701-720, (2007). UR - https://doi.org/10.33773/jum.876269 L1 - https://dergipark.org.tr/en/download/article-file/1562677 ER -