Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MZM_2021_109_6_a8, author = {S. E. Stepanov and I. I. Tsyganok}, title = {Codazzi and {Killing} {Tensors} on a {Complete} {Riemannian} {Manifold}}, journal = {Matemati\v{c}eskie zametki}, pages = {901--911}, publisher = {mathdoc}, volume = {109}, number = {6}, year = {2021}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a8/} }
S. E. Stepanov; I. I. Tsyganok. Codazzi and Killing Tensors on a Complete Riemannian Manifold. Matematičeskie zametki, Tome 109 (2021) no. 6, pp. 901-911. http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a8/
[1] T. Branson, “Spectra of self-gradients on spheres”, J. Lie Theory, 9:2 (1999), 491–506 | MR
[2] E. Stein, G. Weiss, “Generalization of the Cauchy–Riemann equations and representations of the rotation group”, Amer. J. Math, 90 (1968), 163–196 | DOI | MR
[3] S. E. Stepanov, M. V. Smolnikova, “Fundamentalnye differentsialnye operatory pervogo poryadka na vneshnikh i simmetricheskikh formakh”, Izv. vuzov. Matem., 2002, no. 11, 55–60 | MR | Zbl
[4] S. E. Stepanov, M. V. Smolnikova, “Affinnaya differentsialnaya geometriya tenzorov Killinga”, Izv. vuzov. Matem., 2004, no. 11, 82–86 | MR
[5] K. Heil, A. Moroianu, U. Semmelmann, “Killing and conformal Killing tensors”, J. Geom. Phys., 106 (2016), 383–400 | DOI | MR
[6] D. Kramer, Kh. Shtefani, M. Mak-Kallum, E. Kherlt, Tochnye resheniya uravnenii Einshteina, Energoizdat, M., 1982 | MR
[7] M. Eastwood, “Higher symmetries of the Laplacian”, Ann. of Math. (2), 161:3 (2005), 1645–1665 | DOI | MR
[8] K. Hell, Killing and conformal Killing tensors, Ph.D. Thesis, Institut für Geometrie und Topologie der Universität Stugart, 2017
[9] T. Sumitomo, K. Tandai, “Killing tensor fields on the standard sphere and spectra of $SO(n+1)/(SO(n-1)\times SO(2)$ and $O(n+1)/O(n-1)\times O(2)$”, Osaka Math. J., 20:1 (1983), 51–78 | MR
[10] S. E. Stepanov, “Polya simmetricheskikh tenzorov na kompaktnom rimanovom mnogoobrazii”, Matem. zametki, 52:4 (1992), 85–88 | MR | Zbl
[11] N. S. Dairbekov, V. A. Sharafutdinov, “Konformno killingovy simmetrichnye tenzornye polya na rimanovykh mnogoobraziyakh”, Matem. tr., 13:1 (2010), 85–145 | MR
[12] V. A. Sharafutdinov, “Killingovy tenzornye polya na $2$-tore”, Sib. matem. zhurn., 57:1 (2016), 199–221 | DOI | MR
[13] K. Heil, A. Moroianu, U. Semmelmann, “Killing tensors on tori”, J. Geom. Phys., 117 (2017), 1–6 | DOI | MR
[14] K. Heil, T. Jentsch, “A special class of symmetric Killing $2$-tensors”, J. Geom. Phys., 138 (2019), 103–124 | DOI | MR
[15] S. E. Stepanov, V. V. Rodionov, “Dopolnenie k odnoi rabote Zh.-P. Burginona”, Differents. geom. mnogoobrazii figur, 28 (1977), 69–73
[16] H. L. Liu, “Codazzi tensor and the topology of surfaces”, Ann. Global Anal. Geom., 16:2 (1998), 189–202 | DOI | MR
[17] H. L. Liu, U. Simon, C. P. Wang, “Higher order Codazzi tensors on conformally flat spaces”, Beiträge Algebra Geom., 39:2 (1998), 329–348 | MR
[18] J. Leder, A. Schwenk-Schellschmidt, U. Simon, M. Wiehe, “Generating higher order Codazzi tensors by functions”, Geometry and Topology of Submanifolds, IX, World Sci. Publ., River Edge, NJ, 1999, 174–191 | MR
[19] S. E. Stepanov, J. Mikeš, I. G. Shandra, “On higher-order Codazzi tensors on complete Riemannian manifolds”, Ann. Global Anal. Geom., 56:3 (2019), 429–442 | DOI | MR
[20] P. Petersen, Riemannian Geometry, Springer, New York, 2016 | MR
[21] H. Wu, The Bochner Technique in Differential Geometry, Higher Education Press, Beijing, 2017 | MR
[22] A. Besse, Mnogoobraziya Enshteina, T. 1, 2, Mir, M., 1990 | MR | Zbl
[23] J. Mikeš, V. Rovenski, S. E. Stepanov, “An example of Lichnerowicz-type Laplacian”, Ann. Glob. Anal. Geom., 58 (2020), 19–34 | DOI | MR
[24] P. Li, Geometric Analysis, Cambridge Univ. Press, Cambridge, 2012 | MR
[25] Ch. Barbance, “Sur les tenseurs symétriques”, C. R. Acad. Sci. Paris Sér. A, 276 (1973), 387–389 | MR
[26] S. Stepanov, I. Tsyganok, J. Mikeš, “On the Sampson Laplacian”, Filomat, 32:4 (2019), 1059–1070 | DOI | MR
[27] K. Yano, S. Bokhner, Krivizna i chisla Betti, IL, M., 1957 | MR | Zbl
[28] E. Calabi, “An extension of E. Hopf's maximum principle with an application to Riemannian geometry”, Duke Math. J., 25 (1957), 45–56 | DOI | MR
[29] P. Li, R. Schoen, “$L^p$ and mean value properties of subharmonic functions on Riemannian manifolds”, Acta Math., 153:1 (1984), 279–301 | MR
[30] S. A. Scherbakov, “O regulyarnosti radialnogo polya na mnogoobrazii Adamara”, Matem. zametki, 34:4 (1983), 609–623 | MR | Zbl
[31] Sh. Kobayasi, K. Nomidzu, Osnovy differentsialnoi geometrii, T. 2, Nauka, M., 1981 | MR | Zbl
[32] R. G. Bettiol, R. A. E. Mendes, Sectional Curvature and Weitzenböck Formulae, 2017, arXiv: 1708.09033
[33] M. Takeuchi, “Parallel submanifolds of space forms”, Manifolds and Lie Groups, Basel, Birkhäuser, 1981, 429–447 | MR
[34] L. P. Eizenkhart, Rimanova geometriya, IL, M., 1948 | Zbl
[35] D. M. J. Calderbank, “Refined Kato inequalities and conformal weights in Riemannian geometry”, J. Funct. Anal., 173 (2000), 214–255 | DOI | MR
[36] H. Wu, R. E. Green, “Integrals of subharmonic functions on manifolds of nonnegative curvature”, Invent. Math., 27 (1974), 265–298 | DOI | MR
[37] S. T. Yau, “Some function-theoretic properties of complete Riemannian manifold and their applications to geometry”, Indiana Univ. Math. J., 25:7 (1976), 659–679 | DOI | MR
[38] M. Berger, D. Ebin, “Some decompositions of the space of symmetric tensors on a Riemannian manifold”, J. Differential Geometry, 3 (1969), 379–392 | DOI | MR