Hu, Jicheng A kind of integral representation on Riemannian manifolds. (English) Zbl 0953.32003 Wuhan Univ. J. Nat. Sci. 1, No. 1, 14-16 (1996). Summary: We generalize the Bochner-Martinelli integral representation to Riemannian manifolds. Things become quite different in this case. First, we define a kind of Newtonian potential and take the interior product of its gradient to be the integral kernel. Then, we prove that this kernel is harmonic in some sense. At last an integral representative theorem is proved. MSC: 32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) 58C10 Holomorphic maps on manifolds Keywords:Bochner-Martinelli integral representation; Riemannian manifolds; Newtonian potential PDFBibTeX XMLCite \textit{J. Hu}, Wuhan Univ. J. Nat. Sci. 1, No. 1, 14--16 (1996; Zbl 0953.32003) Full Text: DOI References: [1] Jicheng, Hu, Plemelj formulae for Bochner-Martinelli integrals, Acta Math Sci, 15A, 1, 25-33 (1995) · Zbl 0900.32002 [2] Jicheng, Hu, Singular integrals-some topics on the theory and applications (1994), Wuhan: Wuhan University Press, Wuhan [3] Jicheng, Hu, Boundary behavior of Cauchy singular integrals, J of Math(PRC), 15, 1, 97-110 (1995) · Zbl 0887.31004 [4] Norguet, F., Introduction aux fonctions de plusieurs variables complexes (1974), Wuhan: Wuhan University, Wuhan · Zbl 0307.32004 [5] Range, R. M., Holomorphic Functions and Integral Representations in several complex variables (1986), Wuhan: Wuhan University, Wuhan · Zbl 0591.32002 [6] Kobayashi, S.; Nomizu, K., Foundations of differential geometry (1969), Wuhan: John Wiley & Sons, Publisher, Wuhan · Zbl 0175.48504 [7] Narasimhan, R., Analysis on real and complex manifold (1973), Amsterdam: North-Holland, Amsterdam [8] Harvey, R.; Lawson, B., On boundaries of complex analytic variables, I Ann of Math, 102, 233-290 (1975) · Zbl 0317.32017 [9] Ryan, J., Plemelj formulae and transformation associated to plane wave decompositions in complex Clifford analysis, Proc London Math Soc, 64, 1, 70-94 (1992) · Zbl 0774.30050 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.