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Matematicheskie Zametki, 2016, Volume 100, Issue 3, Pages 441–449
DOI: https://doi.org/10.4213/mzm10885 (Mi mzm10885) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Harmonic Transforms of Complete Riemannian Manifolds

S. E. Stepanov, I. I. Tsyganok

Financial University under the Government of the Russian Federation, Moscow
Full-text PDF (484 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm10885
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.
Keywords: polar Riemannian manifold, harmonic transformation, Ricci solitons, vanishing theorems.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00053-а
This work was supported by the Russian Foundation for Basic Research under grant 16-01-00053-a.
Received: 30.07.2015
Revised: 14.02.2016
English version:
Mathematical Notes, 2016, Volume 100, Issue 3, Pages 465–471
DOI: https://doi.org/10.1134/S0001434616090133
Bibliographic databases:
Document Type: Article
UDC: 514.765.25+514.764.216
Language: Russian
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
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm10885
  • https://doi.org/10.4213/mzm10885
  • https://www.mathnet.ru/eng/mzm/v100/i3/p441
    • This publication is cited in the following 4 articles:
    1. Sergey Stepanov, Irina Tsyganok, “On the geometry in the large of Hadamard manifolds”, Filomat, 37:25 (2023), 8473  crossref
    2. 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  crossref
    3. 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  mathnet  crossref
    4. M. S. Najdanovic, “On the problem of geodesic mappings and deformations of generalized Riemannian spaces”, J. Math. Anal. Appl., 452:1 (2017), 634–645  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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