Title:
Intermidiate Ricci, homotopy, and submanifolds of symmetric spaces.
Abstract: In the spirit of combining Riemannian geometry,
topology, and algebra when studying symmetric spaces, we introduce a
new approach to the study and identication of submanifolds of
simply-connected symmetric spaces of compact type based upon the computa-
tion of their k-positive Ricci curvature. We then apply the
"generalized connectedness lemma" by Guijarro-Wilhelm to certain
classes of subanifolds 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.