Dodziuk, Jozef Vanishing theorems for square-integrable harmonic forms. (English) Zbl 0479.53035 Proc. Indian Acad. Sci., Math. Sci. 90, 21-27 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 15 Documents MSC: 53C20 Global Riemannian geometry, including pinching Keywords:complete Riemannian manifold; harmonic form; vanishing theorem; Laplacian PDFBibTeX XMLCite \textit{J. Dodziuk}, Proc. Indian Acad. Sci., Math. Sci. 90, 21--27 (1981; Zbl 0479.53035) Full Text: DOI References: [1] Andreotti, A.; Vesentini, E., Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Publ. Math. IHES, 25, 1-30 (1965) · Zbl 0138.06604 [2] Calabi, E., Matsushima’s theorem in Riemannian and Kählerian geometry, Notices Am. Math. Soc., 10, 505-505 (1963) [3] Calabi, E.; Vesentini, E., On compact locally symmetric Kähler manifolds, Ann. Math., 71, 472-507 (1960) · Zbl 0100.36002 · doi:10.2307/1969939 [4] de Rham, G., Varietiés differentiables (1973), Paris: Hermann, Paris [5] Hitchin, N., Harmonic spinors, Adv. Math., 14, 31-55 (1974) · Zbl 0284.58016 · doi:10.1016/0001-8708(74)90021-8 [6] Lichnerowicz, A., Spineurs harmoniques, CR Acad. Sci. Paris Ser AB, 257, 7-9 (1973) · Zbl 0136.18401 [7] Matsushima, Y., On the first Betti number of compact quotients of higher-dimensional symmetric spaces, Ann. Math., 75, 312-330 (1962) · Zbl 0118.38303 · doi:10.2307/1970176 [8] Vesentini, E., Lectures on Levi convexity (1967), Bombay: Tata Institute of Fundamental Research, Bombay · Zbl 0206.36603 [9] Yano, K.; Bochner, S., Curvature and Betti numbers (1953), Princeton: University Press, Princeton · Zbl 0051.39402 [10] Yau, S. T., Some function theoretic properties of complete Riemannian manifolds and their application to geometry, Indiana Univ. Math. J., 25, 659-670 (1976) · Zbl 0335.53041 · doi:10.1512/iumj.1976.25.25051 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.