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Fundamentalnaya i Prikladnaya Matematika, 2005, Volume 11, Issue 1, Pages 35–84 (Mi fpm797)  

This article is cited in 19 scientific papers (total in 19 papers)

Vanishing theorems in affine, Riemannian, and Lorenz geometries

S. E. Stepanov

Vladimir State Pedagogical University
References:
Abstract: In this survey, we consider one aspect of the Bochner technique, the proof of vanishing theorems by using the Weitzenbock integral formulas, which allows us to extend the technique to pseudo-Riemannian manifolds and equiaffine connection manifolds.
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 141, Issue 1, Pages 929–964
DOI: https://doi.org/10.1007/s10958-007-0024-6
Bibliographic databases:
UDC: 514.75
Language: Russian
Citation: S. E. Stepanov, “Vanishing theorems in affine, Riemannian, and Lorenz geometries”, Fundam. Prikl. Mat., 11:1 (2005), 35–84; J. Math. Sci., 141:1 (2007), 929–964
Citation in format AMSBIB
\Bibitem{Ste05}
\by S.~E.~Stepanov
\paper Vanishing theorems in affine, Riemannian, and Lorenz geometries
\jour Fundam. Prikl. Mat.
\yr 2005
\vol 11
\issue 1
\pages 35--84
\mathnet{http://mi.mathnet.ru/fpm797}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2137428}
\zmath{https://zbmath.org/?q=an:1073.58025}
\elib{https://elibrary.ru/item.asp?id=9025102}
\transl
\jour J. Math. Sci.
\yr 2007
\vol 141
\issue 1
\pages 929--964
\crossref{https://doi.org/10.1007/s10958-007-0024-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846567882}
Linking options:
  • https://www.mathnet.ru/eng/fpm797
  • https://www.mathnet.ru/eng/fpm/v11/i1/p35
  • This publication is cited in the following 19 articles:
    1. Vladimir Rovenski, Sergey Stepanov, Irina Tsyganok, Springer Proceedings in Mathematics & Statistics, 440, Differential Geometric Structures and Applications, 2024, 167  crossref
    2. S. E. Stepanov, I. Mikesh, I. I. Tsyganok, “Obobschennaya tekhnika Bokhnera i ee primenenie k izucheniyu proektivnykh i konformnykh otobrazhenii”, Materialy Mezhdunarodnoi konferentsii «Klassicheskaya i sovremennaya geometriya», posvyaschennoi 100-letiyu so dnya rozhdeniya professora Levona Sergeevicha Atanasyana (15 iyulya 1921 g.—5 iyulya 1998 g.). Moskva, 1–4 noyabrya 2021 g. Chast 4, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 223, VINITI RAN, M., 2023, 112–122  mathnet  crossref
    3. Josef Mikeš, Lenka Rýparová, Sergey Stepanov, Irina Tsyganok, “On the Geometry in the Large of Einstein-like Manifolds”, Mathematics, 10:13 (2022), 2208  crossref
    4. I. Mikesh, S. Formella, I. Ginterleitner, N. I. Guseva, “Nekotorye voprosy geodezicheskikh otobrazhenii prostranstv Einshteina”, Geometriya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 203, VINITI RAN, M., 2021, 50–61  mathnet  crossref
    5. Vladimir Rovenski, Sergey Stepanov, Irina Tsyganok, “A Generalized Bochner Technique and Its Application to the Study of Conformal Mappings”, Axioms, 10:4 (2021), 333  crossref
    6. Josef Mikeš, Vladimir Rovenski, Sergey E. Stepanov, “An example of Lichnerowicz-type Laplacian”, Ann Glob Anal Geom, 58:1 (2020), 19  crossref
    7. Sergey Stepanov, Irina Tsyganok, “Vanishing theorems for harmonic mappings into non-negatively curved manifolds and their applications”, manuscripta math., 154:1-2 (2017), 79  crossref
    8. D. M. Volobuev, N. G. Makarenko, I. S. Knyazeva, “Evolution of the Bochner Laplacian for magnetograms of solar active regions”, Geomagn. Aeron., 56:7 (2016), 886  crossref
    9. I. A. Alexandrova, J. Mikeš, S. E. Stepanov, I. I. Tsyganok, “Theorems of Liuville types in theory mappings of the complete Riemannian manifolds”, J. Math. Sci., 221:6 (2017), 737–744  mathnet  crossref  crossref
    10. S. E. Stepanov, I. A. Alexandrova, I. I. Tsyganok, J. Mikeš, “Conformal Killing forms on totally umbilical submanifolds”, Journal of Mathematical Sciences, 217:5 (2016), 525–539  mathnet  mathnet  crossref
    11. Sergey E. Stepanov, Josef Mikeš, “The generalized Landau–Raychaudhuri equation and its applications”, Int. J. Geom. Methods Mod. Phys., 12:08 (2015), 1560026  crossref
    12. Sergey E. Stepanov, Marek Jukl, Josef Mikeš, Springer Proceedings in Mathematics & Statistics, 85, Algebra, Geometry and Mathematical Physics, 2014, 495  crossref
    13. Sergey E. Stepanov, Marek Jukl, Josef Mikeš, “Vanishing theorems of conformal Killing forms and their applications to electrodynamics in the general relativity theory”, Int. J. Geom. Methods Mod. Phys., 11:09 (2014), 1450039  crossref
    14. Sergey E. Stepanov, Josef Mikeš, “Betti and Tachibana numbers of compact Riemannian manifolds”, Differential Geometry and its Applications, 31:4 (2013), 486  crossref
    15. Sinyukova E.N., Chepok O.L., “O geodezicheskikh otobrazheniyakh v tselom rimanovykh prostranstv, udovletvoryayuschikh nekotorym usloviyam differentsialno-algebraicheskogo kharaktera”, Izvestiya penzenskogo gosudarstvennogo pedagogicheskogo universiteta im. V.G. Belinskogo, 2011, no. 26, 214–221  elib
    16. H. N. Sinyukova, “Geodesic uniqueness in the whole of some generally recurrent Riemannian spaces”, J. Math. Sci., 177:5 (2011), 710–715  mathnet  crossref  mathscinet
    17. S. E. Stepanov, “Curvature and Tachibana numbers”, J. Math. Sci., 172:6 (2011), 901–908  mathnet  crossref  mathscinet
    18. T. V. Zudina, S. E. Stepanov, I. G. Shandra, “Equiaffine mappings”, Russian Math. (Iz. VUZ), 51:8 (2007), 25–32  mathnet  crossref  mathscinet  zmath
    19. S. E. Stepanov, “Some conformal and projective scalar invariants of Riemannian manifolds”, Math. Notes, 80:6 (2006), 848–852  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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