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Intrinsic Problems on Riemannian Manifolds with (f, g, u_(k), α_(k))-structure

Title 
Intrinsic Problems on Riemannian Manifolds with (f, g, u_(k), α_(k))-structure
Other Titles 
(f, g, u_(k), α_(k)) 構造를 가지는 Riemann 多樣體上의 Intrinsic Problems
Authors 
Park, Jae Kyun
Issue Date 
1982
Journal 
연구논문집
Vol. 
Vol.7
Issue 
No. 1
Pages 
179-183
Abstract 
本 論文의 硏究 目的은 (f,g,u_(k), α_(k))構造를 자기는 完備連結인 Riemann 多樣體가 pseudo-normal 또는 normal일 必要條件을 찾고, 그리고 이 多樣體가 槪積空間 S^n(1/√2)×S^(n+1)(1/√2) 또는 이의 射影에 의한 factor 空間 [S^n(1/√2)×S^(n+1)(1/√2)]^*와는 合同이기 爲한 必要充分條件을 찾아 보았다. 主要 定理를 간추려 보면 다음과 같다. [1] almost everywhere로 α^2+β^2+γ^2≠1, α≠0, β≠0, γ≠0인 (f,g,u_(k), α_(k))構造를 자기는 完備連結인 Riemann 多樣體가 세 개의 條件 ∇_jα=k_(ji)u^i-v_j, ∇_jβ=-w_j, ∇_k ∇_ju_i=-g_(kj)u_i+g_(ki)u_j-k_(kj)v_i+k_(ki)v_j+2k(ji)v_k를 滿足하면, 이 多樣體는 pseudo-normal이다. [2] 위의 세 條件에 한 條件 k_(ji)u^i=-v_j를 더 滿足한다면, 이 多樣體는 normal이고, S^n(1/√2)×S^(n+1)(1/√2) 또는 [S^n(1/√2)×S^(n+1)(1/√2)]^*와는 合同이다.
The purpose of this paper is to study sufficient conditions for the(f,g,u_(k), α_(k))-structure to be pseudo-normal or normal, and studying some conditions for a complete and connected Riemannian manifold with (f,g,u_(k), α_(k))-structure to be isometric to S^n(1/√2)×S^(n+1)(1/√2) or [S^n(1/√2)×S^(n+1)(1/√2)]^* (1) Assume that a Riemannian manifold M with (f,g,u_(k), α_(k))-structure satisfies α^2+β^2+γ^2≠1, α≠0, β≠0 and γ≠0 almost everywhere. If there exists a symmetric tensor field k_(ji) of type(0, 2) which satisfies _jα=k_(ji)u^i-v_j, _jβ=-w_j, _k _ju_i=-g_(kj)u_i+g_(ki)u_j-k_(kj)v_i+k_(ki)v_j+2k(ji)v_k. Then M is pseudo-normal. (2) If we add a condition k_(ji)u^i=-v_j to (1), then M is normal, and it is isometric to S^n(1/√2)×S^(n+1)(1/√2) or [S^n(1/√2)×S^(n+1)(1/√2)]^*
URI 
http://repository.uc.ac.kr/handle/2014.oak/772
ISSN 
1598-3390
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03. 교양과 > 연구논문

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