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In this note, we look at estimates for the scalar curvature k of a Riemannian manifold M which are related to spin^c Dirac operators: We show that one may not enlarge a Kaehler metric with positive Ricci curvature without making k smaller somewhere on M. We also give explicit upper bounds for min(k) for arbitrary Riemannian metrics on certain submanifolds of complex projective space. In certain cases, these estimates are sharp: we give examples where equality is obtained.
We establish extremality of Riemannian metrics g with non-negative curvature operator on symmetric spaces M=G/K of compact type with rk(G)-rk(K)le 1. Let g be another metric with scalar curvature k, such that gge g on 2-vectors. We show that kge k ev
We study harmonic maps from a 3-manifold with boundary to $mathbb{S}^1$ and prove a special case of dihedral rigidity of three dimensional cubes whose dihedral angles are $pi / 2$. Furthermore we give some applications to mapping torus hyperbolic 3-manifolds.
The scalar curvature equation for rotation invariant Kahler metrics on $mathbb{C}^n backslash {0}$ is reduced to a system of ODEs of order 2. By solving the ODEs, we obtain complete lists of rotation invariant zero or positive csck on $mathbb{C}^n ba
We classify manifolds of small dimension that admit both, a Riemannian metric of non-negative scalar curvature, and a -- a priori different -- metric for which all wedge products of harmonic forms are harmonic. For manifolds whose first Betti numbers
We study (transverse) scalar curvature type equation on compact Sasaki manifolds, in view of recent breakthrough of Chen-Cheng cite{CC1, CC2, CC3} on existence of Kahler metrics with constant scalar curvature (csck) on compact Kahler manifolds. Follo