Abstract:
Vanishing theorems for harmonic and infinitesimal harmonic transformations of complete Riemannian manifolds are proved. The proof uses well-known Liouville theorems on subharmonic functions on noncompact complete Riemannian manifolds.
Citation:
S. E. Stepanov, I. I. Tsyganok, “Harmonic Transforms of Complete Riemannian Manifolds”, Mat. Zametki, 100:3 (2016), 441–449; Math. Notes, 100:3 (2016), 465–471
This publication is cited in the following 4 articles:
Sergey Stepanov, Irina Tsyganok, “On the geometry in the large of Hadamard manifolds”, Filomat, 37:25 (2023), 8473
I. A. Aleksandrova, S. E. Stepanov, I. I. Tsyganok, “From Harmonic Mappings to Ricci Flows Due to the Bochner Technique”, J Math Sci, 263:3 (2022), 423
I. A. Aleksandrova, S. E. Stepanov, I. I. Tsyganok, “Ot garmonicheskikh otobrazhenii k potokam Richchi na osnove tekhniki Bokhnera”, Materialy mezhdunarodnoi konferentsii “Geometricheskie metody v teorii upravleniya i matematicheskoi fizike”, posvyaschennoi 70-letiyu S.L. Atanasyana, 70-letiyu I.S. Krasilschika, 70-letiyu A.V. Samokhina, 80-letiyu V.T. Fomenko. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 25–28 sentyabrya 2018 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 169, VINITI RAN, M., 2019, 75–87
M. S. Najdanovic, “On the problem of geodesic mappings and deformations of generalized Riemannian spaces”, J. Math. Anal. Appl., 452:1 (2017), 634–645