On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections

1976 ◽  
Vol 2 (1) ◽  
pp. 131-190 ◽  
Author(s):  
Noboru TANAKA
Keyword(s):  
Lie Algebras ◽  
Real Hypersurfaces ◽  
Graded Lie Algebras ◽  
Cartan Connections

REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH GENERALIZED TANAKA–WEBSTER 𝔇⊥-PARALLEL SHAPE OPERATOR

2012 ◽  
Vol 09 (04) ◽  
pp. 1250032 ◽  
Author(s):  
IMSOON JEONG ◽  
HYUNJIN LEE ◽  
YOUNG JIN SUH
Keyword(s):  
Lie Algebras ◽  
Riemannian Manifolds ◽  
Shape Operator ◽  
Variational Problems ◽  
Real Hypersurfaces ◽  
Graded Lie Algebras ◽  
Totally Geodesic ◽  
Cartan Connections ◽  
Parallel Shape Operator ◽  
Kodai Math

In a paper due to [I. Jeong, H. Lee and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster parallel shape operator, Kodai Math. J.34 (2011) 352–366] we have shown that there does not exist a hypersurface in G2(ℂm+2) with parallel shape operator in the generalized Tanaka–Webster connection (see [N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan J. Math.20 (1976) 131–190; S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc.314(1) (1989) 349–379]). In this paper, we introduce a new notion of generalized Tanaka–Webster 𝔇⊥-parallel for a hypersurface M in G2(ℂm+2), and give a characterization for a tube around a totally geodesic ℍ Pn in G2(ℂm+2) where m = 2n.

Cohomology of certain $ \mathbb N$-graded Lie algebras

2004 ◽  
Vol 59 (6) ◽  
pp. 1210-1211
Author(s):  
D V Millionshchikov ◽  
A Fialowski
Keyword(s):  
Lie Algebras ◽  
Graded Lie Algebras

Generators of simple graded Lie algebras of finite growth

2017 ◽  
Vol 148 (2) ◽  
pp. 315-324
Author(s):  
Liming Tang ◽  
Wende Liu
Keyword(s):  
Lie Algebras ◽  
Graded Lie Algebras ◽  
Finite Growth

scholarly journals Graded Lie Algebras of Maximal Class

1997 ◽  
Vol 349 (10) ◽  
pp. 4021-4051 ◽  
Author(s):  
A. Caranti ◽  
S. Mattarei ◽  
M. F. Newman
Keyword(s):  
Lie Algebras ◽  
Maximal Class ◽  
Graded Lie Algebras
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