On the Curvature of K{\"a}hler Manifolds with Zero Ricci Tensor
Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 537-544.

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The behavior of the modulus of the curvature tensor and of the holomorphic sectional curvature on Ricci-flat Kähler manifolds is investigated.
Keywords: Ricci-flat manifold, curvature tensor.
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V. N. Kokarev. On the Curvature of K{\"a}hler Manifolds with Zero Ricci Tensor. Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 537-544. http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a4/

[1] V. N. Kokarev, “O krivizne Richchi-ploskikh kelerovykh mnogoobrazii”, Mezhdunarodnaya nauchnaya konferentsiya “Sovremennaya geometriya i ee prilozheniya”, Izd-vo Kazanskogo un-ta, Kazan, 2017, 73–75

[2] S. T. Yau, “On the Ricci curvature of a compact Kähler manifold and the complex Monge–Ampére equation I”, Comm. Pure Appl. Math., 31:3 (1978), 339–411 | DOI | MR | Zbl

[3] E. Calabi, “Improper affine hyperspheres of convex type and generalization of a theorem by K. Jörgens”, Michigan Math. J., 5 (1958), 105–126 | DOI | MR | Zbl

[4] R. S. Hamilton, “Three manifolds with positive Ricci curvature”, J. Differential Geom., 17:2 (1982), 255–306 | DOI | MR | Zbl

[5] Sh. Kobayasi, K. Nomidzu, Osnovy differentsialnoi geometrii, T. 2, Nauka, M., 1981 | MR | Zbl

[6] A. Besse, Mnogoobraziya Einshteina, T. I, II, Mir, M., 1990 | MR

[7] S. Bando, A. Kasue, H. Nakajima, “On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth”, Invent. Math., 97:2 (1989), 313–349 | DOI | MR | Zbl

[8] L. Bieberbach, “Über die Bewegungsgruppen des Euklidischen Räume”, Math. Ann., 70:3 (1911), 297–336 | DOI | MR | Zbl

[9] L. Bieberbach, “Über die Bewegungsgruppen des Euklidischen Räume (Zweite Abhandlung.) Die Gruppen mit einem endlichen Fundamentalbereich”, Math. Ann., 72:3 (1912), 400–412 | DOI | MR | Zbl

[10] R. L. Bishop, R. Dzh. Krittenden, Geometriya mnogoobrazii, Mir, M., 1967 | MR | Zbl

[11] E. Calabi, “An extension of E. Hopf's maximum principle with an application to Riemannian geometry”, Duke Math. J., 25 (1958), 45–56 | DOI | MR | Zbl