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Mat. Zametki, 2016, Volume 100, Issue 3, Pages 441–449 (Mi mz10885)  

This article is cited in 2 scientific papers (total in 2 papers)

Harmonic Transforms of Complete Riemannian Manifolds

S. E. Stepanov, I. I. Tsyganok

Financial University under the Government of the Russian Federation, Moscow

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.


DOI: https://doi.org/10.4213/mzm10885

Full text: PDF file (484 kB)
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English version:
Mathematical Notes, 2016, 100:3, 465–471

Bibliographic databases:

UDC: 514.765.25+514.764.216
Received: 30.07.2015
Revised: 14.02.2016

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. 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. Ser. Sovrem. mat. i ee pril. Temat. obz., 169, VINITI RAN, M., 2019, 75–87  mathnet  crossref
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