Existence of almost complex structure on Sn

Abstract

이 논문에서는 짝수 실 다양체에서 almost complex structure를 정의하고, 특별히 S^(n)상에서 n값에 따른 almost complex structure의 존재 유무에 대해 다음과 같은 방법을 통하여 연구한다. 직접 almost complex structure를 구축하여서 S^(2), S^(6)상에서는 almost complex structure가 존재함을 보인다. 그리고 벡터장의 Stiefel-Whitney cohomology classes의 개념을 공부하여, n≠2, 6인 경우에는 S^(n)상에서 almost complex structure가 존재하지 않음을 증명한다.;In this thesis, we first introduce an almost complex structure on an even dimensional real manifold. We determine the existence of an almost complex structure on S" depending on n = 1,2,3, .... In order to showing that S^(2) and S^(6) admit almost complex structure, we will construct in an explict manner an almost complex structure on S^(2) and S^(6). And we introduce the Stiefel-Whitney cohomology classes of the vector bundles over manifolds. We will then prove the nonexistence of almost complex structure for S^(n)(n≠ 2,6). Accordingly we can classify almost complex structures on S^(n) for n = 1,2,3, ...