On submanifolds of Sasakian statistical manifolds

Statistical Manifolds ◽

Invariant Submanifolds ◽

Dual Connection ◽

‎In this paper‎, ‎invariant and‎ ‎anti-invariant submanifolds of Sasakian statistical manifolds are studied‎. ‎Necessary and sufficient conditions are given for vanishing the dual connection in the normal bundle‎. ‎Moreover‎, ‎existence of a Kaehlerian structure on invariant hypersurfaces of Sasakian statistical manifolds are proved‎.

Semi-invariant submanifolds of a normal almost paracontact manifold

Filomat ◽

10.2298/fil1715875a ◽

2017 ◽

Vol 31 (15) ◽

pp. 4875-4887 ◽

Cited By ~ 1

Author(s):

Mehmet Atçeken ◽

Siraj Uddin

Keyword(s):

Sufficient Conditions ◽

Fundamental Properties ◽

Invariant Submanifolds ◽

Normal Almost Paracontact Manifold ◽

In this paper, we introduce the notion of semi-invariant submanifolds of a normal almost paracontact manifold. We study their fundamental properties and the particular cases. The necessary and sufficient conditions are given for a submanifold to be invariant or anti-invariant. Also, we give some results for semi-invariant submanifolds of a normal almost paracontact manifold with constant c and we construct an example.

ON f-KENMOTSU MANIFOLDS AND THEIR SUBMANIFOLDS WITH QUARTER SYMMETRIC METRIC CONNECTIONS

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi2004017s ◽

2021 ◽

pp. 1017

Author(s):

Avijit Sarkar ◽

Nirmal Biswas

Keyword(s):

Sufficient Conditions ◽

Kenmotsu Manifold ◽

Totally Geodesic ◽

Kenmotsu Manifolds ◽

Invariant Submanifolds ◽

The object of the present paper is to study invariant submanifolds of f-Kenmotsu manifolds with respect to quarter symmetric metric connections. Some necessary and sufficient conditions for such submanifolds to be totally geodesic have been deduced. Also we construct an example of a submanifold of a five-dimensional f-Kenmotsu manifold to justify our results.

Invariant submanifolds of generalized Sasakian-space-forms

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887818501499 ◽

2018 ◽

Vol 15 (09) ◽

pp. 1850149 ◽

Cited By ~ 2

Author(s):

Shyamal Kumar Hui ◽

Siraj Uddin ◽

ALi H. Alkhaldi ◽

Pradip Mandal

Keyword(s):

Sufficient Conditions ◽

Ricci Solitons ◽

Space Forms ◽

Totally Geodesic ◽

Sasakian Space Forms ◽

Metric Connection ◽

Invariant Submanifolds ◽

Levi Civita Connection ◽

This paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as semi-symmetric metric connection. We provide an example of such submanifolds and obtain many new results including the necessary and sufficient conditions under which the submanifolds are totally geodesic. The Ricci solitons of such submanifolds are also studied.

On invariant submanifolds of paracompact (k;m)-spaces

SERIES III - MATEMATICS, INFORMATICS, PHYSICS ◽

10.31926/but.mif.2020.13.62.2.13 ◽

2021 ◽

Vol 13(62) (2) ◽

pp. 545-560

Author(s):

Sujoy Ghosh ◽

Avijit Sarkar

Keyword(s):

Fundamental Form ◽

Sufficient Conditions ◽

Second Fundamental Form ◽

Invariant Submanifold ◽

Totally Geodesic ◽

Totally Umbilical ◽

The Second Fundamental Form ◽

Invariant Submanifolds ◽

The object of the present paper is to deduce some necessary and sufficient conditions for invariant Submanifolds of paracontact (κ, µ)-spaces to be totally geodesic. We also establish that a totally umbilical invariant submanifold of a paracontact (κ, µ)-manifold is also totally geodesic. Some more necessary and sufficient conditions for a submanifold of a paracontact (κ, µ)-manifold to be totally geodesic have been deduced using parallelity and pseudo parallelity of the second fundamental form. In the last section we obtain some results on paracontact (κ, µ)-manifold with concircular canonical field.

The extinction time of a general birth and death process with catastrophes

Journal of Applied Probability ◽

10.1017/s0021900200116031 ◽

1986 ◽

Vol 23 (04) ◽

pp. 851-858 ◽

Cited By ~ 1

Author(s):

P. J. Brockwell

Keyword(s):

Laplace Transform ◽

Size Distribution ◽

Sufficient Conditions ◽

Death Process ◽

Extinction Time ◽

Birth And Death Process ◽

Different Types ◽

The Laplace Transform ◽

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Does the Concatenated Generalized Matching Law Identify the Necessary and Sufficient Conditions?

PsycEXTRA Dataset ◽

10.1037/e537052012-028 ◽

2004 ◽

Author(s):

James S. MacDonall

Keyword(s):

Sufficient Conditions ◽

Matching Law ◽

Generalized Matching Law ◽

NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30430-2 ◽

1991 ◽

Vol 11 (1) ◽

pp. 65-71 ◽

Cited By ~ 1

Author(s):

Deming Liu

Keyword(s):

Limit Cycles ◽

Existence And Uniqueness ◽

Polynomial System ◽

Sufficient Conditions ◽

Uniqueness Of Limit Cycles ◽

Nonlinear boundary-value problems for degenerate differential-algebraic systems

Ukrainian Mathematical Bulletin ◽

10.37069/1810-3200-2020-17-3-2 ◽

2020 ◽

Vol 17 (3) ◽

pp. 313-324

Author(s):

Sergii Chuiko ◽

Ol'ga Nesmelova

Keyword(s):

Boundary Value Problem ◽

Boundary Value Problems ◽

Algebraic System ◽

Boundary Value ◽

Sufficient Conditions ◽

Weakly Nonlinear ◽

Differential Algebraic System ◽

Linear Differential ◽

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.