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초록· 키워드
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We show that on a compact locally conformal K¨ahler manifold M2n (dim M2n = 2n ≥ 4), M2n is Kahler if and only if its conformal scalar curvature k is not smaller than the scalar curvature s of M2n everywhere.
As a consequence, if a compact locally conformal Kahler manifold M2n is both conformally flat and scalar flat, then M2n is Kahler. In contrast with the compact case, we show that there exists a locally conformal Kahler manifold with k equal to s, which is not Kahler.
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참고문헌 (11)
참고문헌 신청
A. L. Besse / 1987 / Einstein Manifolds / Springer-Verlag
I. Vaisman / 1979 / A theorem on compact locally conformal K¨ahler manifolds / Proc. Amer. Math. Soc. 75 (2) : 279 ~ 283
I. Vaisman / 1980 / Some curvature properties of locally conformal K¨ahler manifolds / Trans. Amer. Math. Soc. 259 (2) : 439 ~ 447
I. Vaisman / 1982 / Some curvature properties of complex surfaces / Ann. Mat. Pura Appl. 132 : 1 ~ 18
J. Kim / 2000 / Rigidity theorems for Einstein-Thorpe metrics / Geom. Dedicata 80 (1) : 281 ~ 287
I. Vaisman / 1979 / A theorem on compact locally conformal K¨ahler manifolds / Proc. Amer. Math. Soc. 75 (2) : 279 ~ 283
I. Vaisman / 1980 / Some curvature properties of locally conformal K¨ahler manifolds / Trans. Amer. Math. Soc. 259 (2) : 439 ~ 447
I. Vaisman / 1982 / Some curvature properties of complex surfaces / Ann. Mat. Pura Appl. 132 : 1 ~ 18
J. Kim / 2000 / Rigidity theorems for Einstein-Thorpe metrics / Geom. Dedicata 80 (1) : 281 ~ 287
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