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Para-Kiihlerian manifolds carrying a pair of concurrent self-orthogonal vector fields by R. ROSCA Dedicated to his friend and colleague E. Sperner on the occa- sion of his 70 tu birthday. Introduction Let M and Tp(M) be an even dimensional C~176 manifold of signature (n, n) and the tangent space to M at p ~M respectivly. Let at be the regular infinitesimal structure defined in the vectorial space R 2" by two subspaces ~" and ~'" of Tt,(M) of the same dimension n. The pair (~", ~'") defines an involutiv automorphism U on R 2n (that U2= + 1)whose eigen vectors corresponding to the eigen values + 1 and - 1 generate the sub- space ~" (positive sub-space of Tp(M)) and ~'" (negative subspace of Tp(M)) respectively. The subspaces ~" and E'" are integrals of a given 2-form 32 = 2~ (o~ ~ +co '~) A A (o~-o~ '~) on M of rank 2n (i.e. 32^c.) ~ 0) that is the restrictions 321~" and I2l~'" are zero. With 32 is associated a quadratic form g = 2~ (r '~) ~(o~-co '~) which is decomposable in n positive squares and in n negative squares. Putting 0 t = o~ ~ +
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Nov 18, 2008
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