On the spectrum of spherical Dirac-type operators

DOI10.1216/RMJ-2013-43-6-1825zbMath1284.53047MaRDI QIDQ2439531

Nicolae Anghel

Publication date: 14 March 2014

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1393336658

zbMATH Keywords

multiplicityspectrumseparation of variablesspherical Dirac operatorclassical Dirac-type operatorEuclidean Dirac operatorGauss-Bonnet-type operatorgraded Clifford representationpolynomial spinor

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spin and Spin({}^c) geometry (53C27) Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) (54A10)

Cites Work

• Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
• \(L^ 2\)-index formulae for perturbed Dirac operators
• On the spectra of Laplace operator on \(\Lambda^*(S^n)\)
• Opérateur de courbure et laplacien des formes différentielles d'une variété riemannienne
• Spectra and eigenforms of the Laplacian on \(S^n\) and \(P^n(C)\)
• Extrinsic bounds for eigenvalues of the Dirac operator
• Analysis of Dirac systems and computational algebra.
• The Dirac operator on space forms of positive curvature
• Möbius invariants for pairs of spheres \((S^m_1,S^l_2)\) in the Möbius space \(S^n\)
• Clifford modules
• Harmonic Function Theory
• Harmonic analysis of the de Rham complex on the sphere.
• The Dirac Operator on Spaces with Conical Singularities and Positive Scalar Curvatures
• Spinor-valued and Clifford algebra-valued harmonic polynomials
• Lower bounds for the eigenvalues of the Dirac operator. I: The hypersurface Dirac operator
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