• Title/Summary/Keyword: symmetric space

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SUFFICIENT CONDITIONS AND CONSTRUCTION OF SYMMETRIC BIBD

  • KANG, SUNGKWON;JUNG, YOON-TAE;LEE, JU-HYUN
    • Honam Mathematical Journal
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    • v.24 no.1
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    • pp.109-119
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    • 2002
  • Some sufficient conditions on the existence and uniqueness of certain symmetric balanced incomplete block design are introduced. Also, a construction algorithm for the design and some examples are presented. The algorithm is developed based on the construction of subspaces of the three-dimensional vector space over a field.

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FIBREWISE INFINITE SYMMETRIC PRODUCTS AND M-CATEGORY

  • Hans, Scheerer;Manfred, Stelzer
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.671-682
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    • 1999
  • Using a base-point free version of the infinite symmetric product we define a fibrewise infinite symmetric product for any fibration $E\;\longrightarrow\;B$. The construction works for any commutative ring R with unit and is denoted by $R_f(E)\;l\ongrightarrow\;B$. For any pointed space B let $G_I(B)\;\longrightarrow\;B$ be the i-th Ganea fibration. Defining $M_R-cat(B):= inf{i\midR_f(G_i(B))\longrihghtarrow\;B$ admits a section} we obtain an approximation to the Lusternik-Schnirelmann category of B which satisfies .g.a product formula. In particular, if B is a 1-connected rational space of finite rational type, then $M_Q$-cat(B) coincides with the well-known (purely algebraically defined) M-category of B which in fact is equal to cat (B) by a result of K.Hess. All the constructions more generally apply to the Ganea category of maps.

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OPTIMAL INEQUALITIES FOR THE CASORATI CURVATURES OF SUBMANIFOLDS OF GENERALIZED SPACE FORMS ENDOWED WITH SEMI-SYMMETRIC METRIC CONNECTIONS

  • LEE, CHUL WOO;LEE, JAE WON;VILCU, GABRIEL-EDUARD;YOON, DAE WON
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1631-1647
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    • 2015
  • In this paper, we prove two optimal inequalities involving the intrinsic scalar curvature and extrinsic Casorati curvature of submanifolds of generalized space forms endowed with a semi-symmetric metric connection. Moreover, we also characterize those submanifolds for which the equality cases hold.

HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KAEHLER MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.32 no.1
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    • pp.119-133
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    • 2017
  • In this paper, we study half lightlike submanifolds of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. First, we characterize the geometry of two types of half lightlike submanifolds of such an indefinite Kaehler manifold. Next, we investigate the geometry of half lightlike submanifolds of an indefinite complex space form with a semi-symmetric non-metric connection.

LIGHTLIKE HYPERSURFACES OF AN INDEFINITE KAEHLER MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Jin, Dae Ho
    • Journal of the Korean Mathematical Society
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    • v.54 no.1
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    • pp.101-115
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    • 2017
  • In this paper, we study three types of lightlike hypersurfaces, which are called recurrent, Lie recurrent and Hopf lightlike hypersurfaces, of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. We provide several new results on such three types of lightlike hypersurfaces of an indefinite Kaehler manifold or an indefinite complex space form, with a semi-symmetric non-metric connection.

ON ALMOST QUASI RICCI SYMMETRIC MANIFOLDS

  • Kim, Jaeman
    • Communications of the Korean Mathematical Society
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    • v.35 no.2
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    • pp.603-611
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    • 2020
  • The purpose of this note is to introduce a type of Riemannian manifold called an almost quasi Ricci symmetric manifold and investigate the several properties of such a manifold on which some geometric conditions are imposed. And the existence of such a manifold is ensured by a proper example.

Tube volumes about geodesic balls

  • Lee, Sung-Yun
    • Communications of the Korean Mathematical Society
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    • v.11 no.1
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    • pp.209-214
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    • 1996
  • A flat space is characterized by tube volumes about geodesic balls. Similar characterizations are also given for other rank one symmetric spaces.

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Equilibrium Point and Stability of Double-Free-Nodes Space Truss Under Symmetric Condition (대칭 조건을 갖는 2-자유절점 공간 트러스의 평형점과 안정성)

  • Ha, Junhong;Shon, Sudeok;Lee, Seungjae;Hwang, Kyung-Ju
    • Journal of Korean Association for Spatial Structures
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    • v.19 no.4
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    • pp.69-76
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    • 2019
  • A stadium roof that uses the pin-jointed spatial truss system has to be designed by taking into account the unstable phenomenon due to the geometrical non-linearity of the long span. This phenomenon is mainly studied in the single-free-node model (SFN) or double-free-node model (DFN). Unlike the simple SFN model, the more complex DFN model has a higher order of characteristic equations, making analysis of the system's stability complicated. However, various symmetric conditions can allow limited analysis of these problems. Thus, this research looks at the stability of the DFN model which is assumed to be symmetric in shape, and its load and equilibrium state. Its governing system is expressed by nonlinear differential equations to show the double Duffing effect. To investigate the dynamic behavior and characteristics, we normalize the system of the model in terms of space and time. The equilibrium points of the system unloaded or symmetrically loaded are calculated exactly. Furthermore, the stability of these points via the roots of the characteristic equation of a Jacobian matrix are classified.

Numerical Investigation on the Mechanism of Mode Transition in Axi-symmetric Supersonic Jet Screech (축대칭 초음속 제트에서 스크리치 모드 전이현상의 수치적 연구)

  • Bin, Jong-Hoon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.38 no.8
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    • pp.790-797
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    • 2010
  • Mode transition of the axi-symmetric screech tone in the low supersonic Mach number range from 1.0 to 1.20 is numerically analyzed. The axi-symmetric Navier-Stokes equations and the k-e turbulence model are solved in the cylindrical coordinate system. The dispersion-relation-preserving(DRP) scheme is applied for space discretization and the optimized four levels marching method are used for time integration. At low supersonic Mach numbers with an axi-symmetric A1 mode in the simulation, it is shown that acoustic propagation due to the nonlinear effects is seen in the lateral direction and the screech tone frequency is the same as the vortex passing frequency due to the generation of intense large-scale vortical motions.