Paper derives sub-Riemannian versions of Kastler-Kalau-Walze and Dabrowski-Sitarz-Zalecki theorems for twisted BCV spaces.
problem Deriving sub-Riemannian versions of the Kastler-Kalau-Walze and Dabrowski-Sitarz-Zalecki theorems for twisted BCV spaces.
method Derives sub-Riemannian versions of the Kastler-Kalau-Walze and Dabrowski-Sitarz-Zalecki theorems for the twisted BCV spaces.
result Computes Connes conformal invariants for the twisted product and sub-Riemannian limits of these invariants for the twisted BCV spaces.
The study classifies biharmonic submersions from 3D BCV spaces.
problem Classifying biharmonic submersions from 3D BCV spaces.
method Complete classification through proving existence and constructing families of submersions.
result Proper biharmonic Riemannian submersions exist only in two specific cases.
The paper extends Bour's theorem to BCV spaces with constant mean curvature helicoids.
problem Generalizing Bour's theorem to helicoidal surfaces in BCV spaces.
method Two-parameter family representation of helicoidal surfaces.
result Characterization of helicoidal surfaces with constant mean curvature.
Study classifies triharmonic surfaces in 3D homogeneous spaces.
problem Classifying triharmonic surfaces in 3D homogeneous spaces.
method Classification through isoparametric and CMC surfaces.
result Complete classification of CMC r-harmonic Hopf cylinders in BCV-spaces.
The differential geometry of 3-dimensional Bianchi, Cartan and Vranceanu (BCV) spaces is well known. We introduce the extended Bianchi, Cartan and Vranceanu (EBCV) spaces as a natural seven dimensional generalization of BCV spaces and study some of their main geometric properties, such as the Levi-Civita connec…
This paper proposed a bias-compensated normalized maximum correntropy criterion (BCNMCC) algorithm charactered by its low steady-state misalignment for system identification with noisy input in an impulsive output noise environment. The normalized maximum correntropy criterion (NMCC) is derived from a correntropy based…
Totally biharmonic hypersurfaces in space forms and 3D BCV spaces classified.
problem Characterizing totally biharmonic hypersurfaces in space forms and 3D BCV spaces.
method Analyzing geodesics and isoparametric properties to classify hypersurfaces.
result Classification of totally biharmonic hypersurfaces in space forms and 3D BCV spaces.
BCV method helps estimate clusters and hyper-parameters in large data sets.
problem Determining the number of clusters in large-scale data.
method Bi-cross validation (BCV) for spectral clustering.
result BCV directly applies to spectral clustering for estimating clusters and hyper-parameters.
Study of harmonic Riemannian submersions from 3D geometries.
problem Characterizing harmonic Riemannian submersions from specific 3D geometries.
method Using generalized integrability data and classifications of Thurston's 3D geometries, 3D BCV spaces, and Berger sphere.
result Complete classifications and explicit constructions of harmonic Riemannian submersions.
Biconservative hypersurfaces are hypersurfaces with conservative stress-energy tensor with respect to the bienergy functional, and form a geometrically interesting family which includes that of biharmonic hypersurfaces. In this paper we study biconservative surfaces in the 3-dimensional Bianchi-Cartan-Vranceanu spaces,…