Differentiable sphere theorems for submanifolds of positive \(k\)-th Ricci curvature. (English) Zbl 1260.53073
P. Hartman introduced the concept of \(k\)-th Ricci curvature in [J. Differ. Equations 34, 326–338 (1979; Zbl 0443.34029)] for Riemannian manifolds. The authors of this paper are motivated by results on minimal submanifolds of spheres (see [S.-T. Yau, Am. J. Math. 96, 346–366 (1974; Zbl 0304.53041); ibid. 97, 76–100 (1975; Zbl 0304.53042); U. Simon, Arch. Math. 29, 106–112 (1977; Zbl 0389.53028)]) and prove several pinching theorems for compact immersed submanifolds of positive \(k\)-th Ricci curvature.
Reviewer: Udo Simon (Berlin)
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