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Der erste Eigenwert des Dirac-Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung. (German) Zbl 0462.53027


MSC:

53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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[1] Berger, Lecture Notes in Mathematics 194 (1971)
[2] und , Spektraleigenschaften des Dirac-Operators – die Fundamentallösung seiner Wärmeleitungsgleichung und die Asymptotenentwicklung der Zeta-Funktion, im Druck in Journal of Differential Geometry. · Zbl 0442.58030
[3] Zur Existenz paralleler Spinorfelder über Riemannschen Mannigfaltigkeiten, Colloquium Mathematicum (im Druck).
[4] und , Ein Kriterium für die formale Selbstadjungiertheit des Dirac-Operators, im Druck in Colloquium Mathematicum.
[5] Gilkey, Journal of Differential Geometry 10 pp 601– (1975)
[6] Gromoll, Lecture Notes in Mathematics 55 (1968)
[7] Hitchin, Advances in Mathematics 11 pp 1– (1974)
[8] Fibre bundles, New York 1966. · Zbl 0144.44804
[9] Ikeda, Osaka Journal of Mathematics 12 pp 173– (1975)
[10] Jensen, Duke Mathematical Journal 42 pp 397– (1975)
[11] Lichnerowicz, C. R. Acad. Sci. Paris 257 pp 7– (1963)
[12] Milnor, L’Enseignement Mathématique pp 198– (1963)
[13] Parthasarathy, Annals of Mathematics 96 pp 1– (1972)
[14] und , Differentialgeometrie und Faserbündel, Berlin 1972.
[15] Berechnung des Spektrums des Quadrates des Dirac-Operators auf der Sphäre, Colloquium Mathematicum (im Druck).
[16] Spaces of constant curvature, New York 1967. · Zbl 0162.53304
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