Automorphisms of projective manifolds
Abstract
Let $(M,P\nabla_M)$ be a compact projective manifold and $Aut(M,P\nabla_M)$ its group of automorphisms. The purpose of this paper is to study the topological properties of $(M,P\nabla_M)$ if $Aut(M,P\nabla_M))$is not discrete by applying the results of [13] and the Benzekri's functor which associates to a projective manifold a radiant affine manifold. This enables us to show that the orbits of the connected component of $Aut(M,P\nabla_M)$ are immersed
projective submanifolds. We also classify $3$-dimensional compact projective manifolds such that $dim(Aut(M,P\nabla_M))\geq 2$.
Downloads
References
Albert A. Structure of algebras. Vol. 24. American Math. Soc. 1939.
Aschenbrenner, M. Friedl, S. Wilton, H. 3 manifold groups. https://arxiv.org/pdf/1205.0202.pdf
Benoist, Y. Nilvarietes projectives. Commentarii Mathematici Helvetici, 1994, vol. 69, no 1, p. 447-473.
Benzecri J.P. Sur les varietes localement affines et localement projectives. Bulletin de la S.M.F. 88 (1960) 229-332.
Bredon, G. Bredon, Glen E. Topology and geometry. Vol. 139. Graduate texts in Math.
Chatelet, Gilles, Rosenberg, Harold, et Weil, Daniel. A classification of the topological types of R2-actions on closed orientable 3-manifolds. Publications Mathematiques de l’IHES, 1974, vol. 43, p. 261-272
Conlon, Lawrence. Transversally parallelizable foliations of codimension two. Transactions of the American Mathematical Society, 1974, vol. 194, p. 79-102.
Cooper, D. Goldman, W. A 3–Manifold with no Real Projective Structure. In Annales de la Faculte des sciences de Toulouse: Mathematiques, vol. 24, no. 5, pp. 1219-1238. 2015
Goldman, W. Convex real projective structures on compact surfaces. J. Differential Geometry 31 (1990) 791-845.
Montgomery D. Samelson H. Transformation groups of spheres. Annals of Mathematics 44 (1943) 454-470.
Montgomery, D. Zippin, L. Topological transformation groups. Interscience Tracts in pure and applied mathematics 1955.
Sullivan, D; Thurston„ W. Manifolds with canonical coordinate charts: some examples. Enseign. Math 29 (1983): 15-25.
Tsemo, A. Dynamique des varietes affines. Journal of the London Mathematical Society 63 (2001) 469-486.
Tsemo, A. Decomposition des varietes affines. Bulletin des sciences math´ematiques 125 (2001) 71-83.
A Tsemo, A. Linear foliations on affine manifolds. Topology and its Applications. (300) 107756.
Copyright (c) 2024 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
