1,040 research outputs found
Curvature dependent lower bounds for the first eigenvalue of the Dirac operator
Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we
derive inequalities that involve a real parameter and join the eigenvalues of
the Dirac operator with curvature terms. The discussion of these inequalities
yields vanishing theorems for the kernel of the Dirac operator and lower
bounds for the spectrum of if the curvature satisfies certain conditions.Comment: Latex2e, 14p
When central sequence C*-algebras have characters
We investigate C*-algebras whose central sequence algebra has no characters,
and we raise the question if such C*-algebras necessarily must absorb the
Jiang-Su algebra (provided that they also are separable). We relate this
question to a question of Dadarlat and Toms if the Jiang-Su algebra always
embeds into the infinite tensor power of any unital C*-algebra without
characters. We show that absence of characters of the central sequence algebra
implies that the C*-algebra has the so-called strong Corona Factorization
Property, and we use this result to exhibit simple nuclear separable unital
C*-algebras whose central sequence algebra does admit a character. We show how
stronger divisibility properties on the central sequence algebra imply stronger
regularity properties of the underlying C*-algebra.Comment: 28 page
Eigenvalue estimates for the Dirac operator depending on the Weyl curvature tensor
We prove new lower bounds for the first eigenvalue of the Dirac operator on
compact manifolds whose Weyl tensor or curvature tensor, respectively, is
divergence free. In the special case of Einstein manifolds, we obtain estimates
depending on the Weyl tensor.Comment: Latex2.09, 9 page
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