The scalar curvature of CR submanifolds of maximal CR dimension

2009 ◽  
pp. 163-167
Author(s):  
Mirjana Djorić ◽  
Masafumi Okumura
Keyword(s):  
Scalar Curvature ◽  
Cr Submanifolds

scholarly journals CR-submanifolds of a locally conformal Kaehler space form

1994 ◽  
Vol 17 (3) ◽  
pp. 511-514
Author(s):  
M. Hasan Shahid
Keyword(s):  
Scalar Curvature ◽  
Sectional Curvature ◽  
Ricci Curvature ◽  
Space Form ◽  
Holomorphic Sectional Curvature ◽  
Totally Geodesic ◽  
Locally Conformal ◽  
Cr Submanifolds

(Bejancu [1,2]) The purpose of this paper is to continue the study ofCR-submanifolds, and in particular of those of a locally conformal Kaehler space form (Matsumoto [3]). Some results on the holomorphic sectional curvature,D-totally geodesic,D1-totally geodesic andD1-minimalCR-submanifolds of locally conformal Kaehler (1.c.k.)-space fromM¯(c)are obtained. We have also discussed Ricci curvature as well as scalar curvature ofCR-submanifolds ofM¯(c).

scholarly journals CR-Submanifolds of Generalized -Space Forms

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Mahmood Jaafari Matehkolaee
Keyword(s):  
Scalar Curvature ◽  
Sectional Curvature ◽  
Upper Bound ◽  
Ricci Tensor ◽  
Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Cr Submanifold ◽  
Special Cases ◽  
Cr Submanifolds

We study sectional curvature, Ricci tensor, and scalar curvature of submanifolds of generalized -space forms. Then we give an upper bound for foliate -horizontal (and vertical) CR-submanifold of a generalized -space form and an upper bound for minimal -horizontal (and vertical) CR-submanifold of a generalized -space form. Finally, we give the same results for special cases of generalized -space forms such as -space forms, generalized Sasakian space forms, Sasakian space forms, Kenmotsu space forms, cosymplectic space forms, and almost -manifolds.

scholarly journals Bounds for generalized normalized δ-Casorati curvatures for Bi-slant submanifolds in T-space forms

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 329-340 ◽  
Author(s):  
Mohd. Aquib
Keyword(s):  
Scalar Curvature ◽  
Space Forms ◽  
Equality Case ◽  
Slant Submanifolds ◽  
Invariant Submanifolds ◽  
Normalized Scalar Curvature ◽  
Cr Submanifolds

In this paper, we prove the inequality between the generalized normalized ?-Casorati curvatures and the normalized scalar curvature for the bi-slant submanifolds in T-space forms and consider the equality case of the inequality. We also develop same results for semi-slant submanifolds, hemi-slant submanifolds, CR-submanifolds, slant submanifolds, invariant and anti-invariant submanifolds in T-space forms.

scholarly journals SCALAR CURVATURE OF CONTACT THREE CR-SUBMANIFOLDS IN A UNIT (4m + 3)-SPHERE

2011 ◽  
Vol 48 (3) ◽  
pp. 585-600
Author(s):  
Hyang-Sook Kim ◽  
Jin-Suk Pak
Keyword(s):  
Scalar Curvature ◽  
Cr Submanifolds

Positive scalar curvature metrics via end-periodic manifolds

2020 ◽  
Vol 5 (3) ◽  
pp. 639-676
Author(s):  
Michael Hallam ◽  
Varghese Mathai
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Positive Scalar

scholarly journals On the quantization of folded strings in non-critical dimensions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jacob Sonnenschein ◽  
Dorin Weissman
Keyword(s):  
Scalar Curvature ◽  
Space Dimension ◽  
Massive Particle ◽  
Open String ◽  
Closed String ◽  
Target Space ◽  
Critical Dimensions ◽  
Complete Set ◽  
Rotating String ◽  
Folding Point

Abstract Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since there is no complete set of normalizable eigenmodes. Furthermore in the non-critical effective string action of Polchinski and Strominger, there is a divergence associated with the folds. We overcome this obstacle by putting a massive particle at each folding point which can be used as a regulator. Using this method we compute the spectrum of quantum fluctuations around the rotating string and the intercept of the leading Regge trajectory. The results we find are that the intercepts are a = 1 and a = 2 for the open and closed string respectively, independent of the target space dimension. We argue that in generic theories with an effective string description, one can expect corrections from finite masses associated with either the endpoints of an open string or the folding points on a closed string. We compute explicitly the corrections in the presence of these masses.

scholarly journals Quaternionic contact 4n + 3-manifolds and their 4n-quotients

2021 ◽  
Author(s):  
Yoshinobu Kamishima
Keyword(s):  
Scalar Curvature ◽  
Lie Group ◽  
Contact Structure ◽  
Einstein Manifolds ◽  
Hermitian Metrics ◽  
Kähler Metric ◽  
Formula One ◽  
Quaternion Space ◽  
Kahler Metric ◽  
Do So

AbstractWe study some types of qc-Einstein manifolds with zero qc-scalar curvature introduced by S. Ivanov and D. Vassilev. Secondly, we shall construct a family of quaternionic Hermitian metrics $$(g_a,\{J_\alpha \}_{\alpha =1}^3)$$ ( g a , { J α } α = 1 3 ) on the domain Y of the standard quaternion space $${\mathbb {H}}^n$$ H n one of which, say $$(g_a,J_1)$$ ( g a , J 1 ) is a Bochner flat Kähler metric. To do so, we deform conformally the standard quaternionic contact structure on the domain X of the quaternionic Heisenberg Lie group$${{\mathcal {M}}}$$ M to obtain quaternionic Hermitian metrics on the quotient Y of X by $${\mathbb {R}}^3$$ R 3 .

scholarly journals Isoperimetry, Scalar Curvature, and Mass in Asymptotically Flat Riemannian 3‐Manifolds

2021 ◽  
Vol 74 (4) ◽  
pp. 865-905
Author(s):  
Otis Chodosh ◽  
Michael Eichmair ◽  
Yuguang Shi ◽  
Haobin Yu
Keyword(s):  
Scalar Curvature ◽  
Asymptotically Flat
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