JP Journal of Geometry and Topology
Volume 5, Issue 2, Pages 155 - 176
(July 2005)
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FOUR-DIMENSIONAL GEOMETRIC STRUCTURES AND ALMOST COMPLEX STRUCTURES - GENERAL PROCEDURE (RIEMANNIAN VERSION) - : I-R
Yasuo Matsushita (Japan)
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Abstract: It is known that among nineteen four-dimensional geometries (in the sense of Thurston), there are fourteen geometries which admit a complex structure compatible with a group of isometries. We focus our attention to the five geometries which do not admit such a complex structure, and analyze if these geometries can admit or not an almost complex structure. We shall analyze the present issue in a series of papers. In this first paper, we discuss the existence problem of an almost complex structure on these five geometries from a general point of view in a series of papers. In this first paper, we discuss general procedure of the present issue. |
Keywords and phrases: geometric structures in dimension four, almost complex structure, opposite almost complex structure, almost Hermitian structure, opposite almost Hermitian structure, almost Kähler structure, opposite almost Kähler structure. |
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