Bochner-Kähler and Bach flat manifolds
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DOI: 10.1007/s00013-019-01356-z
Abstract: We have classified Bochner-Kähler manifolds of real dimension $$> 4$$>4, which are also Bach flat. In the 4-dimensional case, we have shown that if the scalar curvature is harmonic, then it is constant. Finally, we… read more here.
Keywords: flat manifolds; bach flat; hler bach; scalar curvature ... See more keywords
Positive scalar curvature with skeleton singularities
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DOI: 10.1007/s00208-018-1753-1
Abstract: We study positive scalar curvature on the regular part of Riemannian manifolds with singular, uniformly Euclidean ($$L^\infty $$L∞) metrics that consolidate Gromov’s scalar curvature polyhedral comparison theory and edge metrics that appear in the study… read more here.
Keywords: skeleton singularities; curvature skeleton; scalar curvature; positive scalar ... See more keywords
Existence of twisted constant scalar curvature Kähler metrics with a large twist
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DOI: 10.1007/s00209-018-2133-y
Abstract: Suppose that there exist two Kähler metrics $$\omega $$ω and $$\alpha $$α such that the metric contraction of $$\alpha $$α with respect to $$\omega $$ω is constant, i.e. $$\varLambda _{\omega } \alpha = \text {const}$$Λωα=const. We… read more here.
Keywords: hler; constant scalar; hler metrics; twisted constant ... See more keywords
Enlargeability, foliations, and positive scalar curvature
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DOI: 10.1007/s00222-018-0829-6
Abstract: We extend the deep and important results of Lichnerowicz, Connes, and Gromov–Lawson which relate geometry and characteristic numbers to the existence and non-existence of metrics of positive scalar curvature (PSC). In particular, we show: that… read more here.
Keywords: enlargeability foliations; foliations positive; geometry; scalar curvature ... See more keywords
Rigidity of Riemannian manifolds with positive scalar curvature
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DOI: 10.1007/s10455-018-9600-x
Abstract: For the Bach-flat closed manifold with positive scalar curvature, we prove a rigidity theorem involving the Weyl curvature and the traceless Ricci curvature. Moreover, we provide a similar rigidity result with respect to the $$L^{\frac{n}{2}}$$Ln2-norm… read more here.
Keywords: rigidity riemannian; riemannian manifolds; scalar curvature; positive scalar ... See more keywords
Closed Willmore minimal hypersurfaces with constant scalar curvature in S5(1) are isoparametric
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DOI: 10.1016/j.aim.2017.05.002
Abstract: Abstract In this paper, we will prove that any closed minimal Willmore hypersurface M 4 of S 5 with constant scalar curvature must be isoparametric. To be precise, M 4 is either an equatorial 4… read more here.
Keywords: minimal hypersurfaces; constant scalar; willmore minimal; scalar curvature ... See more keywords
Hypersurfaces with constant scalar curvature in space forms
Sign Up to like & getrecommendations! Published in 2018 at "Differential Geometry and Its Applications"
DOI: 10.1016/j.difgeo.2018.01.001
Abstract: Abstract In this paper we study the rigidity of complete hypersurfaces with constant scalar curvature in Riemannian space forms. Under an appropriate constraint on Φ, the traceless part of its second fundamental form, we prove… read more here.
Keywords: scalar curvature; hypersurfaces constant; constant scalar; space forms ... See more keywords
Conformally flat hypersurfaces with constant scalar curvature
Sign Up to like & getrecommendations! Published in 2018 at "Differential Geometry and its Applications"
DOI: 10.1016/j.difgeo.2018.08.002
Abstract: Abstract We classify the conformally flat hypersurfaces f : M 3 → R 4 with three distinct principal curvatures and constant scalar curvature. read more here.
Keywords: constant scalar; hypersurfaces constant; conformally flat; scalar curvature ... See more keywords
Geography of 4-manifolds with positive scalar curvature
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DOI: 10.1016/j.exmath.2021.05.003
Abstract: Abstract We discuss the geography problem of closed oriented 4-manifolds that admit a Riemannian metric of positive scalar curvature, and use it to survey mathematical work employed to address Gromov’s observation that manifolds with positive… read more here.
Keywords: positive scalar; manifolds positive; geography manifolds; scalar curvature ... See more keywords
Compactness of sign-changing solutions to scalar curvature-type equations with bounded negative part
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DOI: 10.1016/j.jde.2018.12.002
Abstract: Abstract We consider the equation Δ g u + h u = | u | 2 ⁎ − 2 u in a closed Riemannian manifold ( M , g ) , where h ∈ C… read more here.
Keywords: scalar curvature; negative part; changing solutions; sign changing ... See more keywords
Beyond Schwarzschild–de Sitter spacetimes. III. A perturbative vacuum with nonconstant scalar curvature in R+R2 gravity
Sign Up to like & getrecommendations! Published in 2022 at "Physical Review D"
DOI: 10.1103/physrevd.107.104009
Abstract: In violation of the generalized Lichnerowicz theorem advocated by Nelson and others, quadratic gravity admits vacua with non-constant scalar curvature. In a recent publication [Phys. Rev. D 106, 104004 (2022)], we revitalized a program that… read more here.
Keywords: gravity; scalar curvature; lichnerowicz theorem; generalized lichnerowicz ... See more keywords