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- W80591277 abstract "Classically, a Kaehler structure consists of a Riemann metric and a complex structure, which are related by well known compatibility conditions. The Riemann metric is then called a Kaehler metric. If a Kaehler metric is allowed to be non-degenerate and non-definite, the concept of indefinite Kaehler structure appears naturally. So, we have a geometry which is, at the same time, complex and semi-Riemannian. Besides its purely mathematical interest, indefinite Kaehler geometry (in the case of index 2) could be seen, from the point of view of Physics, as a synthesis of two important geometries: the Lorentzian geometry of space-time and the symplectic geometry of phase space. The indefinite Kaehler metric is a complex version of the Lorentzian metric and the Kaehler form is a covariant version of the classical symplectic form. It is argued in G. Kaiser [22] that indefinite Kaehler geometry could be a unifying geometry to study holomorphic bundles on complexifications of space-time. M. Barros and the first author [7] systematically introduced indefinite Kaehler manifolds and studied several properties involving their curvature. ∗Supported by MCYT-FEDER Grant BFM2001-2871-C04-01. ∗∗Supported by Grant R14-2002-003-01001-0 from Korea Science and Engineering Foundation." @default.
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- W80591277 date "2004-01-01" @default.
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- W80591277 title "Differential geometry of indefinite complex submanifolds in indefinite complex space forms" @default.
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