Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds
作者： Aliya Naaz Siddiqui , Bang-Yen Chen , Oguzhan Bahadir , None
DOI: 10.3390/MATH7090797
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摘要: Warped products play crucial roles in differential geometry, as well mathematical physics, especially general relativity. In this article, first we define and study statistical solitons on Ricci-symmetric warped R × f N 2 1 . Second, submanifolds of manifolds. For statistically immersed a manifold constant curvature, prove Chen’s inequality involving scalar the squared mean Laplacian warping function (with respect to Levi–Civita connection). At end, establish relationship between curvature Casorati curvatures terms for product same ambient space.
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F. Casorati, Mesure de la courbure des surfaces suivant l'idée commune.: Ses rapports avec lesmesures de courbure gaussienne et moyenne Acta Mathematica. ,vol. 14, pp. 95- 110 ,(1890) , 10.1007/BF02413317
Barbara Opozda, Bochner’s technique for statistical structures Annals of Global Analysis and Geometry. ,vol. 48, pp. 357- 395 ,(2015) , 10.1007/S10455-015-9475-Z
Bang-Yen Chen, None, Warped Products in Real Space Forms Rocky Mountain Journal of Mathematics. ,vol. 34, pp. 551- 563 ,(2004) , 10.1216/RMJM/1181069867
Bang-Yen Chen, Some pinching and classification theorems for minimal submanifolds Archiv der Mathematik. ,vol. 60, pp. 568- 578 ,(1993) , 10.1007/BF01236084
Paul W. Vos, FUNDAMENTAL EQUATIONS FOR STATISTICAL SUBMANIFOLDS WITH APPLICATIONS TO THE BARTLETT CORRECTION Annals of the Institute of Statistical Mathematics. ,vol. 41, pp. 429- 450 ,(1989) , 10.1007/BF00050660
Teodor Oprea, On a Riemannian Invariant of Chen Type Rocky Mountain Journal of Mathematics. ,vol. 38, pp. 567- 581 ,(2008) , 10.1216/RMJ-2008-38-2-567
R. L. Bishop, B. O’Neill, Manifolds of negative curvature Transactions of the American Mathematical Society. ,vol. 145, pp. 1- 49 ,(1969) , 10.1090/S0002-9947-1969-0251664-4
Bang-Yen Chen, None, ON ISOMETRIC MINIMAL IMMERSIONS FROM WARPED PRODUCTS INTO REAL SPACE FORMS Proceedings of the Edinburgh Mathematical Society. ,vol. 45, pp. 579- 587 ,(2002) , 10.1017/S001309150100075X
Vladimir Slesar, Bayram Şahin, Gabriel-Eduard Vîlcu, Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms Journal of Inequalities and Applications. ,vol. 2014, pp. 123- ,(2014) , 10.1186/1029-242X-2014-123
Hitoshi Furuhata, Hypersurfaces in statistical manifolds Differential Geometry and its Applications. ,vol. 27, pp. 420- 429 ,(2009) , 10.1016/J.DIFGEO.2008.10.019