Classification of Flat Lagrangian H-umbilical Submanifolds in Indefinite Complex Euclidean spaces

Yıl 2019, Cilt: 12 Sayı: 2, 268 - 275, 03.10.2019

Shangrong Deng

Öz

In this article, we completely characterize flat Lagrangian H-umbilical submanifolds in the

indefinite complex Euclidean spaces Cns

. Consequently, in conjunction with a result from [4],

Lagrangian H-umbilical submanifolds in the indefinite complex Euclidean n-space Cns

with n > 2

are completely classified.

Anahtar Kelimeler

H-umbilical submanifolds, Lagrangian submanifolds

Kaynakça

• [1] Chen, B.-Y., Geometry of submanifolds and its applications, (Science University of Tokyo, Tokyo, Japan 1981).
• [2] Chen, B.-Y., Interaction of Legendre curves and Lagrangian submanifolds, Israel J. Math. 99 (1997), 69–108.
• [3] Chen, B.-Y., Complex extensors and Lagrangian submanifolds in complex Euclidean spaces, Tohoku Math. J. 49 (1997), 277–297.
• [4] Chen, B.-Y., Representation of flat Lagrangian H-umbilical submanifolds in complex Euclidean spaces, Tohoku Math. J. 51 (1999), 13–20.
• [5] Chen, B.-Y., Complex extensors and Lagrangian submanifolds in indefinite complex Euclidean spaces, Bulletin Math. Inst. AcademiaSinica 31 (2003), 151-179.
• [6] Chen, B.-Y., Pseudo-Riemannian geometry, -invariants and applications, (World Scientific Publications, Hackensack, New Jersey, 2011).
• [7] Chen, B.-Y., A construction method of Lagrangian surfaces in complex pseudo Euclidean plane C21 and its applications, Int. Electron. J. Geom. 7 (2014), 4-25.
• [8] Chen, B.-Y. and Fastenakels, J., Classification of flat Lagrangianl surfaces in complex Lorentzian plane, Acta Mathematica Sinica, 23, No.12(2007), 2111-2144.
• [9] Deng, S., Lagrangian H-umbilical surfaces in complex Lorentzian plane, Int. Electron. J. Geom. 9, No. 2 (2016), 87-93.
• [10] Deng, S., Classification of Lagrangian H-umbilical surfaces of constant curvature in complex Lorentzian plane, Int. Electron. J. Geom. 10,No. 1 (2017), 48-57.
• [11] B. O’Neill, Semi-Riemannian geometry with applications to relativity, (Academic Press, New York, 1983).
• [12] R. Ponge and H. Reckziegel, Twisted products in pseudo-Riemannian geometry, Geometriae Dedicata 48, (1993), 15-25.
• [13] K. Yano and M. Kon, Structures on manifolds, (World Scientific Publishing Co., Singapore, 1984).