A geometric proof of the Berger Holonomy Theorem

By C. Olmos. 2005

48 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d40c71dea08d6fc9c7a01bf5e3efeda444c9cfe3

Citations in the corpus

• Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “In the Riemannian case a new geometric proof of Berger’s Theorem is now available [ Olm05 ].”
• Classification of manifolds with weakly 1/4-pinched curvatures (2007, unknown): “(g(t)) = SU(m) (iv) n= 4m≥ 8 and Hol(g(t)) = Sp(m) (v) n= 4m≥ 8 and Hol(g(t)) = Sp(m) ·Sp(1) (vi) n= 7 and Hol(g(t)) = G2 (vii) n= 8 and Hol(g(t)) = Spin(7) (see e.g. [8], Theorem 3.4.1; see also [1],[13],[14]). The fact that (M,g(t)) has positive Ricci curvature precludes cases (iii),(iv),(vi),(vii”