Tuesday 22 November 2022, 16:00 - 17:00 in HG00.310
Masoumeh Zarei (Münster)
Intermediate Ricci, homotopy, and submanifolds of symmetric spaces
In the spirit of combining Riemannian geometry, topology, and algebra when studying symmetric spaces, we introduce a new approach to the study and identification of submanifolds of simply-connected symmetric spaces of compact type based upon the computation of their \(k\)-positive Ricci curvature. We then apply the "generalized connectedness lemma" by Guijarro-Wilhelm to certain classes of submanifolds of symmetric spaces, including totally geodesic ones, to show that within certain codimension ranges such submanifolds have the same "Cartan type" as their ambient spaces, (possibly) up to product with spheres. This is joint work with Manuel Amann and Peter Quast.