Projective Geometry I: Principles and Properties
نویسنده
چکیده
The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection. After a brief historical background, this paper presents and analyses the projective Cartan and Tractor connections, the various structures they can preserve, and their geometric interpretations. Preserved subbundles of the Tractor bundle generate foliations with Ricci-flat leaves. Contact-, CR-, HR-, and Einstein-structures arise from other reductions of the Tractor holonomy.
منابع مشابه
Institute for Mathematical Physics Projective Holonomy I: Principles and Properties Projective Holonomy I: Principles and Properties
The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection. After a brief historical background, this paper presents and analyses the projective Cartan and Tractor connections, the various structures they can preserve, and their geometric interpretations. Preserved subbundles of the Tractor bundle generate foliations with Ricci-f...
متن کاملTriple factorization of non-abelian groups by two maximal subgroups
The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...
متن کاملVeblen on Projective Relativity 191 Veblen on Projective Relativity
This book by Professor Veblen is a result of a series of lectures given at the University of Göttingen during the summer of 1932. I t deals with that new aspect of the theory of relativity which is often called projective relativity on account of its relation to projective geometry. I t allows a unified theory of the gravitational and the electromagnetic field, and, though it is not referred to...
متن کاملA Constructive Real Projective Plane
The classical theory of plane projective geometry is examined constructively, using both synthetic and analytic methods. The topics include Desargues's Theorem, harmonic conjugates, projectivities, involutions, conics, Pascal's Theorem, poles and polars. The axioms used for the synthetic treatment are constructive versions of the traditional axioms. The analytic construction is used to verify t...
متن کاملProof of Some Notable Properties with Which Solids Enclosed by Plane Faces Are Endowed
Just as plane rectilinear figures, whose nature is commonly investigated in Geometry, have certain well known general properties, such as that the number of angles is equal to the number of sides and that the sum of the angles is equal to a number of right angles which is four less than twice the number of sides, so have I recently outlined the first principles of a Solid Geometry of the same t...
متن کامل