Journal ArticleDOI
On a generalization of the hopf fibration, III (Subvarieties in theC-spaces)
TLDR
In this paper, the inherited fibration structure of the fiber torus has been studied in terms of the curvature form of a connection when C-spaces are considered as the toral bundle space over an algebraic variety.Abstract:
Analytic subvarieties inC-spaces are discussed. First, a certain kind of closed 2-formdω is constructed. Then, the subvarieties are studied by means of this 2-form.dω may be considered as the curvature form of a connection whenC-spaces are considered as the toral bundle space over an algebraic variety. This 2-form is horizontal in its nature with respect to the bundle structure and indicates, in general, how different the bundle is from the trivial bundle. Because of this twist in the bundle space, subvarieties in theC-spaces tend to inherit the same structure. In this paper, the inherited fibration structure is studied. The most concrete results are obtained when the fiber torus has complex dimension 2.read more
References
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Book
Principles of Algebraic Geometry
Phillip Griffiths,Joe Harris +1 more
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
Book
Differential Geometry and Symmetric Spaces
TL;DR: In this article, the classification of symmetric spaces has been studied in the context of Lie groups and Lie algebras, and a list of notational conventions has been proposed.