Peibiao Zhao

Bio: Peibiao Zhao is an academic researcher from Nanjing University of Science and Technology. The author has contributed to research in topics: Manifold & Riemann curvature tensor. The author has an hindex of 3, co-authored 7 publications receiving 61 citations.

On semi-symmetric metric connection in sub-Riemannian manifold

Abstract: The authors firstly in this paper define a semi-symmetric metric non-holonomic connection (in briefly, SS-connection) on sub-Riemannian manifolds. An invariant under a SS-connection transformation is obtained. The authors then further give a result that a sub-Riemannian manifold $(M,V_{0},g,\bar{ abla})$ is locally horizontally flat if and only if $M$ is horizontally conformally flat and horizontally Ricci flat.

Some Invariants of Quarter-Symmetric Metric Connections Under the Projective Transformation

Abstract: This paper studies the characteristics of quarter-symmetric metric connections. Some invariants with respect to the projective transformation are obtained.

Ricci semisymmetric almost kenmotsu manifolds with nullity distributions

Abstract: The object of the present paper is to characterize Ricci semisymmetric almost Kenmotsu manifolds with its characteristic vector field \xi belonging to the (k,\mu )^{`}-nullity distribution and (k,\mu )-nullity distribution respectively. Finally, an illustrative example is given.

Geometric and physical characteristics of mixed super quasi-Einstein manifolds

Abstract: The authors consider a mixed super quasi-Einstein manifold, which is conducive to understanding deeply the global characteristics of the universe including its topology. Firstly, the existence of s...

A Class of Non-Holonomic Projective Connections on Sub-Riemannian Manifolds

Abstract: The authors define a semi-symmetric non-holonomic(SSNH)-projective connection on sub-Riemannian manifolds and find an invariant of the SSNH-projective transformation. The authors further derive that a sub-Riemannian manifold is of projective flat if and only if the Schouten curvature tensor of a special SSNH-connection is zero.

Introduction to Mathematical Finance

Abstract: Outline: This is the first part of a two-semester sequence course on mathematical finance. In the Fall semester, we will examine the fundamental principles of financial derivatives from both financial and mathematical perspectives, and demonstrate how the mathematical tools from stochastic calculus, differential equations and numerical methods join forces to form an essential part in modern finance. The emphasis of the course is a mathematical understanding of the intrinsic relationships among various financial instruments, which serves as a basis for investment decisions and trading strategies. The central theme of the Fall semester is the classic Black-Scholes-Merton model, and we plan to give a thorough treatment of the original model, with extensive discussions on the practical extensions in response to various disadvantages of the original model. One of the most intuitive and transparent approaches to illustrate that is also extensively used in practice is the binomial tree model. It contains most of the essential idea of the Black-Scholes-Merton methodology, and it can be naturally extended to build more general continuous-time models. Time permitting, we will include as much real life examples as possible to make this a rewarding experience for those who plan to pursue a career in this direction, as well as those who are just intrigued by the subject and its impact on our society.

Optimal inequalities for the Casorati curvatures of submanifolds of real space forms endowed with semi-symmetric metric connections

Abstract: In this paper, we prove two optimal inequalities involving the intrinsic scalar curvature and extrinsic Casorati curvature of submanifolds of real space forms endowed with a semi-symmetric metric connection. Moreover, we show that in both cases, the equality at all points characterizes the invariantly quasi-umbilical submanifolds.

ON A SEMI-SYMMETRIC METRIC CONNECTION IN AN (ε)-KENMOTSU MANIFOLD

Abstract: . The object of the present paper is to study a semi-symmetricmetric connection in an (e)-Kenmotsu manifold. In this paper, we studya semi-symmetric metric connection in an (e)-Kenmotsu manifold whoseprojective curvature tensor satisfies certain curvature conditions. 1. IntroductionThe idea of a semi-symmetric linear connection on a differentiable manifoldwasfirstintroducedby Friedmannand Schouten[11] in 1924. Hayden[12] intro-duced a semi-symmetric metric connection on a Riemannian manifold. Yano[21] proved the theorem: A Riemannian manifold admits a semi-symmetricmetric connection whose curvature tensor vanishes if and only if Riemannianmanifold is conformally flat. Semi-symmetric metric connections on a Rie-mannian manifold have been studied by Amur and Pujar [1], Pravanovic [15],Binh [4], De ([6], [7]), De and Biswas [8], Sharfuddin and Hussain [16], Pathakand De [14], Jun, De and Pathak [13], Barman and De [2], Chaubey and Ojha[5], Singh and Pandey [17], Singh, Pandey and Pandey ([18], [19]) and manyothers.Duggal and Sharma [10] studied a semi-symmetric metric connection in asemi-Riemannian manifold. They studied some properties of the Ricci tensor,affine conformal motions, geodesics and group manifolds with respect to thesemi-symmetric metric connection. On the other hand, the study of manifoldswith indefinite metrics is of interest from the standpoint of physics and relativ-ity. Manifolds with indefinite metrics have been studied by several authors. In1993, Bejancu and Duggal [3] introduced the concept of (e)-Sasakian manifoldsand Xufeng and Xiaoli [20] established that these manifolds are real hypersur-faces of indefinite Kahlerian manifolds. Recently De and Sarkar [9] introduced

Casorati Inequalities for Submanifolds in a Riemannian Manifold of Quasi-Constant Curvature with a Semi-Symmetric Metric Connection

Abstract: By using new algebraic techniques, two Casorati inequalities are established for submanifolds in a Riemannian manifold of quasi-constant curvature with a semi-symmetric metric connection, which generalize inequalities obtained by Lee et al. J. Inequal. Appl. 2014, 2014, 327.