Author:
Jianwei Zhou Department of Mathematics, Suzhou University Suzhou~215006, P.R.~China Suzhou~215006, P.R.~China

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Summary  

We study minimal and totally geodesic submanifolds in Lie groups and related problems. We show that: (1) The imbedding of the Grassmann manifold GF(n,N) in the Lie group GF(N) defined naturally makes GF(n,N) a totally geodesic submanifold; (2) The imbedding S7SO(8) defined by octonians makes S7a totally geodesic submanifold inSO(8); (3) The natural inclusion of the Lie group GF(N) in the sphere ScN^2-1(√N) of gl(N,F)is minimal. Therefore the natural imbedding GF(N)→gl(N,F)is formed by the eigenfunctions of the Laplacian on GF(N).

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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