极小模原理的一类三阶全对称张量不等式应用
Application of the Minimal Normal Tensors to a Class of Third-Order Fully Symmetric Tensor Inequalities
摘要: 本文研究了共形形式Φ消失的三阶全对称张量Ai,j,k的极小模张量，我们利用极小模的非负性证明了不等式。
Abstract: In this paper, we study the minimal norm tensors of the third order full symmetry tensors Ai,j,k, with vanishes from the conformal form Φ. We prove the inequality by using the non-negativity of the minimal norm.
文章引用：段德园, 龚一帆. 极小模原理的一类三阶全对称张量不等式应用[J]. 理论数学, 2024, 14(2): 649-654. https://doi.org/10.12677/PM.2024.142064

参考文献

[1] Cheng, Q.M. and Ishikawa, S. (1999) A Characterization of the Clifford Torus. Proceedings of the American Mathe-matical Society, 127, 819-828. [Google Scholar] [CrossRef] 
[2] Alexander, J.W. (1926) On the Decomposition of Tensors. Annals of Mathematics, 27, 421-423. [Google Scholar] [CrossRef] 
[3] Krupka, D. (1995) The Trace Decomposition Problem. Beitragezur Algebra und Geometrie, 36, 303-316.
[4] Krupka, D. (2017) Decompositions of Covariant Tensor Spaces. Lepage Research Institute Library, 3, 1-20.
[5] Krupka, D. (2003) The Weyl Tensors. Publicationes Mathematicae Debrecen, 62, 447-460. [Google Scholar] [CrossRef] 
[6] Krupka, D. (1995) The Trace Decomposition Problem. Beitragezur Algebra und Geometrie, 36, 303-316.
[7] Krupka, D. (1996) The Trace Decomposition of Tensors of Type (1,2) and (1,3). In: Tamássy, L. and Szenthe, J., Eds., New Developments in Differential Geometry, Springer, Dordrecht, 243-253. [Google Scholar] [CrossRef] 
[8] Mikes, J., Jukl, M. and Juklová, L. (2011) Some Results on Traceless Decomposition of Tensors. Journal of Mathematical Sciences, 174, 627-640. [Google Scholar] [CrossRef] 
[9] Mikes, J. (1996) On the General Trace Decomposition Problem. Proceedings of Conference, 28 August-1 September 1995, 45-50.
[10] Jukl, M. and Juklová, L. (2013) On Decompo-sition Problems on Manifolds with a Special Differential Operators. Miskolc Mathematical Notes, 14, 591-599. [Google Scholar] [CrossRef] 
[11] Lakomá, L. and Jukl, M. (2004) The Decomposition of Tensor Spaces with Almost Complex Structure. In: Slovák, J. and Čadek, M., Eds., Proceedings of the 23rd Winter School “Geometry and Physics”, Circolo Matematico di Palermo, Palermo, 145-150.
[12] Toth, V.T. and Turyshev, S.G. (2022) Efficient Trace-Free Decomposition of Symmetric Tensors of Arbitrary Rank. International Journal of Geometric Methods in Modern Physics, 19, Article ID: 2250201. [Google Scholar] [CrossRef] 
[13] Guo, Z. and Guan, S.L. (2021) Minimal Norm Tensors Principle and its Applications. arXiv preprint arXiv:2112.01222.
[14] Wang, C. (1998) Moebius Geometry of submanifolds in Sn. manuscripta mathematica, 96, 517-534.
https://Doi.Org/10.1007/S002290050080
[15] Li, H.Z. and Wang, C.P. (2003) Surfaces with Vanishing Möbius form in Sn. Acta Mathematica Sinica, 19, 671-678. [Google Scholar] [CrossRef] 
[16] Liu, H., Wang, C. and Zhao, G. (2001) Möbius Isotropic Submanifolds in Sn. Tohoku Mathematical Journal, 53, 553-569. [Google Scholar] [CrossRef] 
[17] Guom Z., Lim, T., Linm, L., et al. (2011) Classification of Hypersurfaces with Constant Möbius Curvature in Sm+1. Mathematische Zeitschrift, 271, 193-219. [Google Scholar] [CrossRef] 
[18] Li, H. and Wang, C. (2003) Möbius Geometry of Hypersurfaces with Constant Mean Curvature and Scalar Curvature. manuscripta mathematica, 112, 1-13. [Google Scholar] [CrossRef] 
[19] 钟定兴, 肖卫玲, 张和颜. 上具有两个Blaschke特征值的超曲面[J]. 赣南师范大学学报, 2017, 38(6): 37-42.
[20] 李兴校, 宋虹儒. 单位球面中具有3个不同Blaschke特征值的Blaschke平行子流形[J]. 数学年刊A辑(中文版), 2018, 39(3): 249-272.
[21] Guo, Z. and Li, H. (2018) Conformal Invariants of Submanifolds in a Riemannian Space and Conformal Rigidity Theorems on Willmore Hypersurfaces. The Journal of Geometric Analysis, 28, 2670-2691. [Google Scholar] [CrossRef] 

为你推荐