ISSN:
1436-5081
Keywords:
53A15
;
Complex affine immersions
;
complex analytic Riemannian manifold
;
H-projective flatness
;
dualH-projective flatness
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Two geometric versions of the fundamental theorem for non-degenerate complex affine hypersurface immersions are proved. We consider non-degenerate complex affine hypersurface immersions with complex transversal connection form (or equivalently, with holomorphic normalization) and prove that the conormal map is a holomorphic map. These considerations inspired the definitions of complex semi-compatible and complex semi-conjugate connections. This allows us to formulate the integrability conditions of the fundamental theorem, on one hand in terms of the induced connection, which has to be complex semi-compatible and dualH-projective flat, and on the other hand, in terms of its semi-conjugate connection, which has to beH-projective flat. Using this results, we formulate the conditions of the fundamental theorem in terms of anyH-projective flat complex affine connection.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01326767
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