The 𝐿²-harmonic forms on rotationally symmetric Riemannian manifolds revisited

Anghel, N.

doi:10.1090/S0002-9939-05-07947-5

The $L^2$-harmonic forms on rotationally symmetric Riemannian manifolds revisited
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Proc. Amer. Math. Soc. 133 (2005), 2461-2467 Request permission

Abstract:

We use separation of variables for generalized Dirac operators on rotationally symmetric Riemannian manifolds to recover a theorem of Dodziuk regarding the spaces of $L^2$-harmonic forms on such manifolds.

References

N. Anghel, $L^2$-index formulae for perturbed Dirac operators, Comm. Math. Phys. 128 (1990), no. 1, 77–97. MR 1042444
Hyeong In Choi, Characterizations of simply connected rotationally symmetric manifolds, Trans. Amer. Math. Soc. 275 (1983), no. 2, 723–727. MR 682727, DOI 10.1090/S0002-9947-1983-0682727-4
Christopher B. Croke, Riemannian manifolds with large invariants, J. Differential Geometry 15 (1980), no. 4, 467–491 (1981). MR 628339
Jozef Dodziuk, $L^{2}$ harmonic forms on rotationally symmetric Riemannian manifolds, Proc. Amer. Math. Soc. 77 (1979), no. 3, 395–400. MR 545603, DOI 10.1090/S0002-9939-1979-0545603-8
Mikhael Gromov and H. Blaine Lawson Jr., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math. 58 (1983), 83–196 (1984). MR 720933
R. E. Greene and H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Mathematics, vol. 699, Springer, Berlin, 1979. MR 521983
Peter March, Brownian motion and harmonic functions on rotationally symmetric manifolds, Ann. Probab. 14 (1986), no. 3, 793–801. MR 841584
Michel Marias, Eigenfunctions of the Laplacian on rotationally symmetric manifolds, Trans. Amer. Math. Soc. 350 (1998), no. 11, 4367–4375. MR 1616007, DOI 10.1090/S0002-9947-98-02354-X