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We show that any orthogonal almost complex structure on a warped product Riemannian manifold of an oriented closed surface with nonnegative Gaussian curvature and a round 4-sphere is never integrable. This provides a partial answer to a question raised by E. Calabi.
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참고문헌 (7)
참고문헌 신청
R. L. Bishop / 1969 / Manifolds of negative curvature / Trans. Amer. Math. Soc 145:1~49
E. Calabi / 1958 / Construction and properties of some 6-dimensional almost complex manifold / Trans. Amer. Math. Soc 87:407~438
어은희 / 2013 / Orthogonal almost complex structures on the Riemannian products of even-dimensional round spheres / 대한수학회지 50(2):231~240
A. Gray / 1976 / Curvature identities for Hermitian and almost Hermitian manifolds / Tohoku Math 28(4):601~612
S. Salamon / 1985 / Harmonic and holomorphic maps, Geometry Seminar, “Luigi Bianchi” II–1984 / Lecture Notes in Math 1164:161~224
E. Calabi / 1958 / Construction and properties of some 6-dimensional almost complex manifold / Trans. Amer. Math. Soc 87:407~438
어은희 / 2013 / Orthogonal almost complex structures on the Riemannian products of even-dimensional round spheres / 대한수학회지 50(2):231~240
A. Gray / 1976 / Curvature identities for Hermitian and almost Hermitian manifolds / Tohoku Math 28(4):601~612
S. Salamon / 1985 / Harmonic and holomorphic maps, Geometry Seminar, “Luigi Bianchi” II–1984 / Lecture Notes in Math 1164:161~224
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