98 research outputs found
Deformation of Hypersurfaces Preserving the Moebius Metric and a Reduction Theorem
A hypersurface without umbilics in the n+1 dimensional Euclidean space is
known to be determined by the Moebius metric and the Moebius second fundamental
form up to a Moebius transformation when n>2. In this paper we consider Moebius
rigidity for hypersurfaces and deformations of a hypersurface preserving the
Moebius metric in the high dimensional case n>3. When the highest multiplicity
of principal curvatures is less than n-2, the hypersurface is Moebius rigid.
Deformable hypersurfaces and the possible deformations are also classified
completely. In addition, we establish a Reduction Theorem characterizing the
classical construction of cylinders, cones, and rotational hypersurfaces, which
helps to find all the non-trivial deformable examples in our classification
with wider application in the future.Comment: 51 pages. A mistake in the proof to Theorem 9.2 has been fixed.
Accepted by Adv. in Mat
Stability manifolds of Kuznetsov components of prime Fano threefolds
Let be a cubic threefold, quartic double solid or Gushel--Mukai
threefold, and be its Kuznetsov
component. We show that a stability condition on is
Serre-invariant if and only if its homological dimension is at most . As a
corollary, we prove that all Serre-invariant stability conditions on
form a contractible connected component of the stability
manifold.Comment: 19 pages, comments are very welcome
M\"{o}bius Homogeneous Hypersurfaces in
Let denote the M\"{o}bius transformation group
of the -dimensional sphere . A hypersurface is called a M\"{o}bius homogeneous hypersurface if there
exists a subgroup of such that the orbit
. In this paper, the M\"{o}bius homogeneous
hypersurfaces are classified completely up to a M\"{o}bius transformation of
.Comment: 35 pages, comments welcom
Bioinformatic Analyses of Subgroup-A Members of the Wheat bZIP Transcription Factor Family and Functional Identification of TabZIP174 Involved in Drought Stress Response
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