scholarly journals A classification of 3-dimensional η-Einstein paracontact metric manifolds

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3567-3573
Author(s):  
Simeon Zamkovoy ◽  
Assen Bojilov
Keyword(s):  
Sectional Curvature ◽  
Constant Sectional Curvature ◽  
3 Dimensional

We show that a 3??dimensional ?-Einstein paracontact metric manifold is either a manifold with trh2 = 0, flat or of constant _??sectional curvature k , ??1 and constant '-sectional curvature ??k , 1.

scholarly journals On the characteristic connection of gwistor space

2013 ◽  
Vol 11 (1) ◽  
Author(s):  
Rui Albuquerque
Keyword(s):  
Sectional Curvature ◽  
Constant Sectional Curvature ◽  
Base Manifold ◽  
Characteristic Connection

AbstractWe give a brief presentation of gwistor spaces, which is a new concept from G 2 geometry. Then we compute the characteristic torsion T c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and deduce the condition under which T c is ∇c-parallel; this allows for the classification of the G 2 structure with torsion and the characteristic holonomy according to known references. The case of an Einstein base manifold is envisaged.

scholarly journals A Note on Surfaces in Space Forms with Pythagorean Fundamental Forms

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 444
Author(s):  
Muhittin Evren Aydin ◽  
Adela Mihai
Keyword(s):  
Sectional Curvature ◽  
Present Note ◽  
Dimensional Space ◽  
Golden Ratio ◽  
Gauss Curvature ◽  
Constant Sectional Curvature ◽  
Round Sphere ◽  
Space Forms ◽  
Totally Umbilical ◽  
3 Dimensional

In the present note we introduce a Pythagorean-like formula for surfaces immersed into 3-dimensional space forms M 3 ( c ) of constant sectional curvature c = − 1 , 0 , 1 . More precisely, we consider a surface immersed into M 3 c satisfying I 2 + II 2 = III 2 , where I , II and III are the matrices corresponding to the first, second and third fundamental forms of the surface, respectively. We prove that such a surface is a totally umbilical round sphere with Gauss curvature φ + c , where φ is the Golden ratio.

Classification of 3-dimensional left-invariant almost paracontact metric structures

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Giovanni Calvaruso ◽  
Antonella Perrone
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Complete Classification ◽  
Natural Assumption ◽  
Geometric Properties ◽  
3 Dimensional ◽  
Metric Structures

AbstractWe study left-invariant almost paracontact metric structures on arbitrary three-dimensional Lorentzian Lie groups. We obtain a complete classification and description under a natural assumption, which includes relevant classes as normal and almost para-cosymplectic structures, and we investigate geometric properties of these structures.

Homogeneous Einstein Finsler Metrics on -dimensional Spheres

2018 ◽  
Vol 62 (3) ◽  
pp. 509-523
Author(s):  
Libing Huang ◽  
Xiaohuan Mo
Keyword(s):  
Sectional Curvature ◽  
Ricci Curvature ◽  
Einstein Metrics ◽  
Constant Sectional Curvature ◽  
Einstein Metric ◽  
Finsler Metrics ◽  
Dimensional Sphere ◽  
Order Ordinary Differential Equation ◽  
Canonical Metric ◽  
Homogeneous Einstein Metrics

AbstractIn this paper, we study a class of homogeneous Finsler metrics of vanishing $S$-curvature on a $(4n+3)$-dimensional sphere. We find a second order ordinary differential equation that characterizes Einstein metrics with constant Ricci curvature $1$ in this class. Using this equation we show that there are infinitely many homogeneous Einstein metrics on $S^{4n+3}$ of constant Ricci curvature $1$ and vanishing $S$-curvature. They contain the canonical metric on $S^{4n+3}$ of constant sectional curvature $1$ and the Einstein metric of non-constant sectional curvature given by Jensen in 1973.

scholarly journals On the classification of 3-dimensionalSL2(ℂ)-varieties

2000 ◽  
Vol 157 ◽  
pp. 129-147 ◽  
Author(s):  
Stefan Kebekus
Keyword(s):  
Automorphism Group ◽  
Semisimple Group ◽  
Picard Number ◽  
Projective Varieties ◽  
3 Dimensional

In the present work we describe 3-dimensional complexSL2-varieties where the genericSL2-orbit is a surface. We apply this result to classify the minimal 3-dimensional projective varieties with Picard-number 1 where a semisimple group acts such that the generic orbits are 2-dimensional.This is an ingredient of the classification [Keb99] of the 3-dimensional relatively minimal quasihomogeneous varieties where the automorphism group is not solvable.

The Value of 3-Dimensional Gel Instillation Sonohysterography in the Detection and Classification of Intracavitary Uterine Abnormalities

2009 ◽  
Vol 16 (6) ◽  
pp. S7
Author(s):  
M. Bij de Vaate ◽  
J. Huirne ◽  
J.W. Van der Slikke ◽  
J. Bartholomew ◽  
H. Brölmann
Keyword(s):  
3 Dimensional

Computerized identification and classification of stance phases as made by front or hind feet of walking cows based on 3-dimensional ground reaction forces

2013 ◽  
Vol 90 ◽  
pp. 7-13 ◽  
Author(s):  
F. Skjøth ◽  
V.M. Thorup ◽  
O.F. do Nascimento ◽  
K.L. Ingvartsen ◽  
M.D. Rasmussen ◽  
...  
Keyword(s):  
Ground Reaction Forces ◽  
3 Dimensional ◽  
Reaction Forces

scholarly journals Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 246
Author(s):  
Yan Zhao ◽  
Wenjie Wang ◽  
Ximin Liu
Keyword(s):  
Sectional Curvature ◽  
Three Dimensional ◽  
Sasakian Manifold ◽  
Constant Sectional Curvature ◽  
Ricci Operator ◽  
Cosymplectic Manifold

Let M be a three-dimensional trans-Sasakian manifold of type ( α , β ) . In this paper, we obtain that the Ricci operator of M is invariant along Reeb flow if and only if M is an α -Sasakian manifold, cosymplectic manifold or a space of constant sectional curvature. Applying this, we give a new characterization of proper trans-Sasakian 3-manifolds.

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