Decompositions of para-complex vector bundles and para-complex affine immersions |
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Authors: | Marie Amélie Lawn Lars Schäfer |
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Affiliation: | 1. Mathematisches Institut, Universit?t Bonn, Beringstra?e 1, D-53115, Bonn, Germany 2. Institut élie Cartan de Mathématiques, Université Henri Poincaré - Nancy 1, B.P. 239, F-54506, Vand?uvre-lès-Nancy Cedex, France
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Abstract: | In this work we study decompositions of para-complex and para-holomorphic vector-bundles endowed with a connection ? over a para-complex manifold. First we obtain results on the connections induced on the subbundles, their second fundamental forms and their curvature tensors. In particular we analyze para-holomorphic decompositions. Then we introduce the notion of para-complex affine immersions and apply the above results to obtain existence and uniqueness theorems for para-complex affine immersions. This is a generalization of the results obtained by Abe and Kurosu [AK] to para-complex geometry. Further we prove that any connection with vanishing (0, 2)-curvature, with respect to the grading defined by the para-complex structure, induces a unique para-holomorphic structure. |
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