scholarly journals Projective flatness in the quantisation of bosons and fermions

2015 ◽  
Vol 56 (7) ◽  
pp. 072102
Author(s):  
Siye Wu
Keyword(s):  
Projective Flatness

Projective flatness of a new class of ( α , β ) (\alpha,\beta) -metrics

2019 ◽  
Vol 26 (1) ◽  
pp. 133-139
Author(s):  
Laurian-Ioan Pişcoran ◽  
Vishnu Narayan Mishra
Keyword(s):  
Riemannian Metric ◽  
Real Scalar ◽  
New Class ◽  
Alpha Beta ◽  
Beta 2 ◽  
Projective Flatness ◽  
The Relationship

Abstract In this paper we investigate a new {(\alpha,\beta)} -metric {F=\beta+\frac{a\alpha^{2}+\beta^{2}}{\alpha}} , where {\alpha=\sqrt{{a_{ij}y^{i}y^{j}}}} is a Riemannian metric; {\beta=b_{i}y^{i}} is a 1-form and {a\in(\frac{1}{4},+\infty)} is a real scalar. Also, we investigate the relationship between the geodesic coefficients of the metric F and the corresponding geodesic coefficients of the metric α.

scholarly journals How a projectively flat geometry regulates F(R)-gravity theory?

2021 ◽  
Author(s):  
Tee-How Loo ◽  
Avik De ◽  
Sanjay Mandal ◽  
P. K. Sahoo
Keyword(s):  
Matter Field ◽  
Gravity Theory ◽  
Gravity Models ◽  
Spacetime Geometry ◽  
Projectively Flat ◽  
Expansion Scalar ◽  
Isotropic Pressure ◽  
Constant Energy Density ◽  
Projective Flatness

Abstract In the present paper we examine a projectively flat spacetime solution of F(R)-gravity theory. It is seen that once we deploy projective flatness in the geometry of the spacetime, the matter field has constant energy density and isotropic pressure. We then make the condition weaker and discuss the effects of projectively harmonic spacetime geometry in F(R)-gravity theory and show that the spacetime in this case reduces to a generalised Robertson-Walker spacetime with a shear, vorticity, acceleration free perfect fluid with a specific form of expansion scalar presented in terms of the scale factor. Role of conharmonic curvature tensor in the spacetime geometry is also briefly discussed. Some analysis of the obtained results are conducted in terms of couple of F(R)-gravity models.

PROJECTIVE STRUCTURES AND -CONNECTIONS

2018 ◽  
Vol 19 (2) ◽  
pp. 571-579
Author(s):  
Radu Pantilie
Keyword(s):  
Projective Space ◽  
Twistor Space ◽  
Projective Structure ◽  
Projective Structures ◽  
Quaternionic Projective Space ◽  
Quaternionic Manifold ◽  
Projective Flatness ◽  
Complex Projective Structure ◽  
Complex Projective

We extend T. Y. Thomas’s approach to projective structures, over the complex analytic category, by involving the $\unicode[STIX]{x1D70C}$-connections. This way, a better control of projective flatness is obtained and, consequently, we have, for example, the following application: if the twistor space of a quaternionic manifold $P$ is endowed with a complex projective structure then $P$ can be locally identified, through quaternionic diffeomorphisms, with the quaternionic projective space.

scholarly journals Riemannian manifolds satisfying certain conditions on pseudo-projective curvature tensor

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 721-731 ◽  
Author(s):  
Sinem Güler ◽  
Sezgin Demirbağ
Keyword(s):  
Curvature Tensor ◽  
Riemannian Manifolds ◽  
Einstein Manifold ◽  
Einstein Manifolds ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Projective Flatness

In this paper we determine some properties of pseudo-projective curvature tensor denoted by ?P on some Riemannian manifolds, especially on generalized quasi Einstein manifolds in the sense of Chaki. Firstly, we consider a pseudo-projectively Ricci semisymmetric generalized quasi Einstein manifold. After that, we study pseudo-projective flatness of this manifold. Moreover, we construct a non-trivial example for a generalized quasi Einstein manifold to prove the existence.

scholarly journals The Chern character of the Verlinde bundle over ℳ¯ g,n

2017 ◽  
Vol 2017 (732) ◽  
pp. 147-163 ◽  
Author(s):  
Alina Marian ◽  
Dragos Oprea ◽  
Rahul Pandharipande ◽  
Aaron Pixton ◽  
Dimitri Zvonkine
Keyword(s):  
Explicit Formula ◽  
Chern Class ◽  
Chern Character ◽  
Conformal Blocks ◽  
Verlinde Formula ◽  
Fusion Algebra ◽  
Chern Characters ◽  
First Chern Class ◽  
Projective Flatness

Abstract We prove an explicit formula for the total Chern character of the Verlinde bundle of conformal blocks over \overline{\mathcal{M}}_{g,n} in terms of tautological classes. The Chern characters of the Verlinde bundles define a semisimple CohFT (the ranks, given by the Verlinde formula, determine a semisimple fusion algebra). According to Teleman’s classification of semisimple CohFTs, there exists an element of Givental’s group transforming the fusion algebra into the CohFT. We determine the element using the first Chern class of the Verlinde bundle on the interior {\mathcal{M}}_{g,n} and the projective flatness of the Hitchin connection.

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