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Remarks on some almost Hermitian structure on the tangent bundle

Takuya Koike, Takashi Oguro, Norio Watanabe

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Abstract

In [5], M. Tahara and Y. Watanabe constructed a family of almost Hermitian structures\n(J,G) on the tangent bundle TM of a Riemannian manifold and constructed a\nfamily of Hermitian and Kähler structure on the tangent bundle on a space form. It is\nwell-known that there are sixteen classes of almost Hermitian manifolds ([3]). In this\npaper, we give the conditions for (J,G) such that TM belongs to each of\nthese sixteen classes.

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In [5], M. Tahara and Y. Watanabe constructed a family of almost Hermitian structures\n(J,G) on the tangent bundle TM of a Riemannian manifold and constructed a\nfamily of Hermitian and Kähler structure on the tangent bundle on a space form. It is\nwell-known that there are sixteen classes of almost Hermitian manifolds ([3]). In this\npaper, we give the conditions for (J,G) such that TM belongs to each of\nthese sixteen classes.

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Available abstract

In [5], M. Tahara and Y. Watanabe constructed a family of almost Hermitian structures\n(J,G) on the tangent bundle TM of a Riemannian manifold and constructed a\nfamily of Hermitian and Kähler structure on the tangent bundle on a space form. It is\nwell-known that there are sixteen classes of almost Hermitian manifolds ([3]). In this\npaper, we give the conditions for (J,G) such that TM belongs to each of\nthese sixteen classes.

Key concepts: Tangent bundle, Hermitian matrix, Mathematics, Hermitian manifold, Tangent, Pure mathematics, Unit tangent bundle, Line bundle

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