By Demeter Krupka;Olga Krupkova;Jan Slovak
This quantity comprises invited lectures and chosen study papers within the fields of classical and sleek differential geometry, international research, and geometric tools in physics, offered on the tenth foreign convention on Differential Geometry and its purposes (DGA2007), held in Olomouc, Czech Republic. The booklet covers fresh advancements and the newest ends up in the next fields: Riemannian geometry, connections, parabolic geometries, jets, differential invariants, the calculus of adaptations on manifolds, differential equations, Finsler buildings, and geometric equipment in physics. it's also a party of the three hundredth anniversary of the delivery of 1 of the best mathematicians, Leonhard Euler, and comprises the Euler lecture "Leonhardt Euler - three hundred years on". The amazing participants comprise: A Asada, Manuel de Leon, Jurgen Eichhorn, J-H Eschenburg, and Ivan Kolar.
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Extra resources for Differential Geometry and its Applications: Proceedings of the 10th International Conference Dga 2007 Olomouc, Czech Republic 27-31 August 2007
Example text
Einstein metrics on SO(n)/SO(n − 2) are completely classified. If n = 3 the group SO(3) has a unique Einstein metric. If n ≥ 5 it was shown by A. Y. Hsiang10 that SO(n)/SO(n − 2) admits exactly one homogeneous invariant Einstein metric. The same result was obtained by M. V. Alekseevsky, I. Dotti, and C. 12 We also refer to Ref. 727-728 for further discussion. For k ≥ 3 there is no obstruction for existence of more than two homogeneous invariant Einstein metrics on Stiefel manifolds SO(n)/SO(n − k).
Math. Soc. 36 (1999) 135–249. 11. E. J. Tipler, Maximal hypersurfaces and foliations of constant mean curvature in general relativity, Phys. Rep. 66 (1980) 109–139. 12. W. P´erez, Conformal properties on classical minimal surface theory, In: Surveys in Differential Geometry (Volume IX: Eigenvalues of Laplacians and other geometric operators, (A. T. ) International Press). 13. J. P´erez, Parabolicity and minimal surfaces, Proceedings of the 2002 Summer School“The global theory of minimal surfaces” (Clay Mathematical Institute & University of California at Berkeley, MSRI), to appear.
1 does not imply in principle that, under the same hypothesis on M , any entire maximal graph in M 2 × R1 must be totally geodesic. However, we can prove the following non-parametric version of our Calabi-Bernstein theorem. 2 (Ref. 3). Let M 2 be a complete Riemannian surface with non-negative Gaussian curvature, KM ≥ 0. Then any entire maximal graph Σ(u) in M 2 × R1 is totally geodesic. In addition, if KM > 0 at some point on M , then u is constant. 2 (Ref. 4). Let M 2 be a complete non-flat Riemannian surface with non-negative Gaussian curvature, KM ≥ 0.