Screen invariant lightlike hypersurfaces of almost product-like statistical manifolds and locally product-like statistical manifolds
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https://doi.org/10.26637/mjm1104/004Abstract
Screen invariant lightlike hypersurfaces of almost product-like statistical manifolds and locally product-like statistical manifolds are introduced. The main formulas and relations are presented for these hypersurfaces. Concurrent and recurrent vector fields are investigated and some characterizations are obtained for screen invariant lightlike hypersurfaces.
Keywords:
Concurrent vector field, lightlike hypersurface, statistical manifoldMathematics Subject Classification:
53C05, 53C25, 53C55- Pages: 363-377
- Date Published: 01-10-2023
- Vol. 11 No. 04 (2023): Malaya Journal of Matematik (MJM)
O. AKSU , M. G¨ ULBAHAR AND E. E RKAN , Lightlike hypersurfaces of almost productlike semi-Riemannian manifolds, Symmetry, 15(2023), 77. DOI: https://doi.org/10.3390/sym15010077
S. A MARI , Differential-geometrical methods in statistics, Lecture Notes in Statistics. vol. 28. Springer-Verlag, New York, (1985). DOI: https://doi.org/10.1007/978-1-4612-5056-2
C. A TINDOGBE , J.-P. E ZIN AND J. T OSSA , Pseudo-inversion of degenerate metrics, Int. J. Math. Math. Sci., 55(2003), 3479—3501. DOI: https://doi.org/10.1155/S0161171203301309
M. E. AYDIN , A. MIHAI AND I. M IHAI , Generalized Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature, Bull. Math. Sci., 7(2017), 155–166. DOI: https://doi.org/10.1007/s13373-016-0086-1
H. A YTIMUR , M. K ON , A. M IHAI , C. OZG ¨ UR AND K. T AKANO , Chen inequalities for statistical submanifolds of Kähler-like statistical manifolds, Mathematics, 7(2019), 1202. DOI: https://doi.org/10.3390/math7121202
O. B AHADIR AND M. M. T RIPATHI , Geometry of lightlike hypersurfaces of a statistical manifold, arXiv
preprint arXiv:1901.09251, (2019).
E. E RKAN , K. T AKANO AND M. G¨ ULBAHAR , Locally product-like statistical manifolds and their hypersurfaces, Int. Electron. J. Geom., 16(2)(2023), 435–450. DOI: https://doi.org/10.36890/iejg.1307467
K. L. D UGGAL AND A. B EJANCU , Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and its applications, Kluwer Academic Publishers Group: Dordrecht, The Netherlands, (1996). DOI: https://doi.org/10.1007/978-94-017-2089-2_5
K. L. D UGGAL AND B. SAHIN , Differential geometry of lightlike submanifolds. In frontiers in mathematics, Birkhauser Verlag: Basel, Switzerland, (2010). DOI: https://doi.org/10.1007/978-3-0346-0251-8
H. F ARAJI , S. A ZAMI AND G. F ASIHI -R AMANDI , h-Almost Ricci solitons with concurrent potential fields, AIMS Math., 5(5)(2020), 4220–4228. DOI: https://doi.org/10.3934/math.2020269
H. F URUHATA , Hypersurfaces in statistical manifolds, Differential Geom. Appl., 27(3)(2009), 420–429. DOI: https://doi.org/10.1016/j.difgeo.2008.10.019
H. F URUHATA , Statistical hypersurfaces in the space of Hessian curvature zero, Differential Geom. Appl., 29(1)(2011), S86–S90. DOI: https://doi.org/10.1016/j.difgeo.2011.04.012
E. K ILIC ¸, M. G¨ULBAHAR AND E. K AVUK , Concurrent vector fields on lightlike hypersurfaces, Mathematics, 9(1)(2021), 59. DOI: https://doi.org/10.3390/math9010059
Y. L I , S. D EY , S. P AHAN AND A. A LI , Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry, Open Math., 20(1)(2022), 574–589. DOI: https://doi.org/10.1515/math-2022-0048
M. S. L ONE , O. B AHADIR , C. P ARK AND I. H WANG , Basic inequalities for statistical submanifolds in Golden-like statistical manifolds, Open Math., 20(1)(2022), 153–166. DOI: https://doi.org/10.1515/math-2022-0017
A. N. S IDDIQUI , B. Y. C HEN AND M. D. S IDDIQI , Chen inequalities for statistical submersions between statistical manifolds, Int. J. Geom. Methods Mod. Phys., 18(04)(2021), 2150049. DOI: https://doi.org/10.1142/S0219887821500493
A. N. S IDDIQUI , M. D. S IDDIQI AND A. H. A LKHALDI , Bounds for statistical curvatures of submanifolds in Kenmotsu-like statistical manifolds, Mathematics, 10(2)(2022), 176. DOI: https://doi.org/10.3390/math10020176
K. O GIUE , On concurrent structures, In Kodai Mathematical Seminar Reports. Department of Mathematics, Tokyo Institute of Technology, 20(1)(1968), 103–106. DOI: https://doi.org/10.2996/kmj/1138845598
K. T AKANO , Statistical manifolds with almost contact structures and its statistical submersions, J. Geom., 85(1-2)(2006), 171–187. DOI: https://doi.org/10.1007/s00022-006-0052-2
K. T AKANO , Statistical manifolds with almost complex structures, Tensor New Ser., 72(3)(2010), 225–231.
A. D. V ILCU AND G. E. V ILCU , Statistical manifolds with almost quaternionic structures and quaternionic Kähler-like statistical submersions, Entropy, 17(9)(2015), 6213–6228. DOI: https://doi.org/10.3390/e17096213
K. Y ANO , Sur le parallélisme et la concourance dans l’espace de Riemann, Proceedings of the Imperial Academy, 19(4)(1943), 189—197. DOI: https://doi.org/10.3792/pia/1195573583
K. Y ANO AND B.-Y. C HEN (1971). On the concurrent vector fields of immersed manifolds, In Kodai Mathematical Seminar Reports, Department of Mathematics, Tokyo Institute of Technology, 23(3)(1971), 343–350. DOI: https://doi.org/10.2996/kmj/1138846372
H. I. Y OLDAS , S¸. E. M ERIC ¸ AND E. Y AS ¸ AR , On generic submanifold of Sasakian manifold with concurrent vector field, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2)(2019), 1983–1994. DOI: https://doi.org/10.31801/cfsuasmas.445788
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