The focus of this paper is to characterize the Lorentzian manifolds equipped with a semi-symmetric non-metric ρ-connection [briefly, (M,̃)]. The conditions for a Lorentzian manifold to be a generalized Robertson–Walker spacetime are established and vice versa. We prove that an n-dimensional compact (M,̃) is geodesically complete. We also study the properties of almost Ricci solitons and gradient almost Ricci solitons on Lorentzian manifolds and Yang pure space, respectively. Finally, we study the properties of semisymmetric (M,̃), and it is proven that (M,̃) is semisymmetric if and only if it is a Robertson–Walker spacetime.

1.
A.
Friedmann
and
J. A.
Schouten
,
Math. Z.
21
,
211
223
(
1924
).
2.
H. A.
Hayden
,
Proc. London Math. Soc.
s2–34
,
27
50
(
1932
).
3.
E.
Pak
,
J. Korean Math. Soc.
6
,
23
31
(
1969
).
4.
K.
Yano
,
Rev. Roum. Math. Pures Appl.
15
,
1579
1586
(
1970
).
5.
N. S.
Agashe
and
M. R.
Chafle
,
Indian J. Pure Appl. Math.
23
,
399
(
1992
).
6.
S. K.
Chaubey
and
A.
Yildiz
,
Turk. J. Math.
43
,
1887
1904
(
2019
).
7.
T.
Wu
and
Y.
Wang
,
Symmetry
13
,
79
(
2021
).
8.
B.
O’Neill
,
Semi-Riemannian Geometry with Applications to the Relativity
(
Academic Press
,
1983
).
9.
L. J.
Alías
,
A.
Romero
, and
M.
Sánchez
,
Gen. Relativ. Gravitation
27
,
71
84
(
1995
).
10.
L. J.
Alías
,
A.
Romero
, and
M.
Sánchez
, “
Compact spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes
,” in
Geometry and Topology of Submanifolds, VII
(
World Scientific
,
1995
).
11.
C. A.
Mantica
and
L. G.
Molinari
,
Int. J. Geom. Methods Mod. Phys.
14
,
1730001
(
2017
).
12.
M.
Sánchez
,
Gen. Relativ. Gravitation
30
,
915
932
(
1998
).
13.
M.
Sánchez
,
J. Geom. Phys.
31
,
1
15
(
1999
).
14.
B.-Y.
Chen
,
Gen. Relativ. Gravitation
46
,
1833
(
2014
).
15.
L. J.
Alías
,
F. J. M.
Estudillo
, and
A.
Romero
,
Classical Quantum Gravity
13
,
3211
3219
(
1996
).
16.
S. K.
Chaubey
,
J. Phys. Math.
10
,
1000303
(
2019
).
17.
S.
Deshmukh
and
I.
Al-Dayel
,
Int. J. Geom. Methods Mod. Phys.
18
,
2150132
(
2021
).
18.
R.
Deszcz
and
M.
Kucharski
,
Tsukuba J. Math.
23
,
113
130
(
1999
).
19.
K. L.
Duggal
,
Int. Scholarly Res. Not.
2016
,
9312525
.
20.
C. A.
Mantica
and
L. G.
Molinari
,
J. Math. Phys.
57
,
102502
(
2016
).
21.
A.
Romero
,
R. M.
Rubio
, and
J. J.
Salamanca
,
Classical Quantum Gravity
30
,
115007
(
2013
).
22.
A.
Romero
and
R. M.
Rubio
,
Ann. Global Anal. Geom.
37
,
21
31
(
2010
).
23.
A.
Fialkow
,
Trans. Am. Math. Soc.
45
,
443
473
(
1939
).
24.
K. L.
Duggal
and
R. S.
Sharma
,
Symmetries of Spacetimes and Riemannian Manifolds
(
Kluwer Academic Publishers
,
1999
).
25.
S. K.
Chaubey
,
Y. J.
Suh
, and
U. C.
De
,
Anal. Math. Phys.
10
,
61
(
2020
).
26.
Y.
Kamishima
,
J. Differ. Geom.
37
,
569
601
(
1993
).
27.
A.
Romero
and
M.
Sánchez
,
Proc. Am. Math. Soc.
123
,
2831
2833
(
1995
).
28.
A.
Romero
and
M.
Sánchez
,
Geom. Dedicata
53
,
103
117
(
1994
).
29.
S. K.
Chaubey
and
Y. J.
Suh
,
Int. J. Geom. Methods Mod. Phys.
18
,
2150209
(
2021
).
30.
J.
Eells
and
J. H.
Sampson
,
Am. J. Math.
86
,
109
160
(
1964
).
31.
R.
Hamilton
,
Contemp. Math.
71
,
237
261
(
1988
).
32.
R.
Hamilton
,
J. Differ. Geom.
17
,
255
306
(
1982
).
33.
A.
Barros
and
E.
Ribeiro
, Jr.
,
Proc. Am. Math. Soc.
140
,
1033
1040
(
2012
).
34.
J. T.
Cho
,
Int. J. Geom. Methods Mod. Phys.
10
,
1220022
(
2013
).
35.
S.
Deshmukh
,
Int. J. Geom. Methods Mod. Phys.
16
,
1950073
(
2019
).
36.
A.
Ghosh
,
Chaos Solitons Fractals
44
,
647
650
(
2010
).
37.
G.
Perelman
, arXiv:math/0211159,
1
39
(
2002
).
38.
P.
Topping
,
Lectures on the Ricci Flow
, Lecture Note Series (
London Mathematical Society; Cambridge University Press
,
2006
).
39.
C. N.
Yang
,
Phys. Rev. Lett.
33
,
445
447
(
1974
).
40.
B. S.
Guilfoyle
and
B. C.
Nolan
,
Gen. Relativ. Gravitation
30
,
473
495
(
1998
).
41.
K. L.
Duggal
,
J. Math. Phys.
33
,
2989
2997
(
1992
).
42.
S. K.
Chaubey
,
J. W.
Lee
, and
S. K.
Yadav
,
J. Korean Math. Soc.
56
,
1113
1129
(
2019
).
43.
S. K.
Chaubey
and
U. C.
De
,
J. Geom. Phys.
157
,
103846
(
2020
).
44.
S. K.
Chaubey
and
U. C.
De
,
Quaestiones Math.
45
,
765
778
(
2021
).
45.
S. K.
Chaubey
,
U. C.
De
, and
M. D.
Siddiqi
,
J. Geom. Phys.
166
,
104269
(
2021
).
46.
E. M.
Patterson
,
J. London Math. Soc.
s1–27
,
287
295
(
1952
).
47.
Z. I.
Szabó
,
J. Differ. Geom.
17
,
531
582
(
1982
).
48.
M.
Brozos-Vázquez
,
E.
García-Río
, and
R.
Vázquez-Lorenzo
,
J. Math. Phys.
46
,
022501
(
2005
).
49.
B.-Y.
Chen
,
Pseudo-Riemannian Geometry, δ-Invariants and Applications
(
World Scientific
,
2011
).
50.
I.
Eriksson
and
J. M. M.
Senovilla
,
Classical Quantum Gravity
27
,
027001
(
2010
).
51.
D.
Kramer
,
H.
Stephani
,
E.
Herlt
, and
M. A. H.
MacCallum
,
Exact Solutions of Einstein’s Field Equations
(
Cambridge University Press
,
1980
).
You do not currently have access to this content.