• Honam Mathematical Journal
• /
• v.45 no.4
• /
• pp.629-647
• /
• 2023

We introduce the study of a new class of a lightlike submersion d. Then, we derive a relationship between the holomorphic section 𝜙 : K₁ → K' from a screen generic lightlike submanifold of an indefinite Kaehler manifold K₂ onto an indefinite almost Hermitian manifold K', and show that for this case K' must be an indefinite Kaehler manifold. Then, we derive a relationship between the holomorphic sectional curvatures of K₂ and K'. Finally, we present a classification theorem for a screen generic lightlike submersion, giving the relationship between the sectional curvatures of the total space K₂ and the fibers.

• Communications of the Korean Mathematical Society
• /
• v.25 no.3
• /
• pp.451-456
• /
• 2010

In this paper, we construct explicitly K$\ddot{a}$hler metrics on the ellipsoids and calculate their sectional curvatures. Using MAPLE [3], we obtain some geodesic curves on an ellipsoid so that if some conditions are dropped in Question 2.1 [4], then Question 2.1 is not true.

• Honam Mathematical Journal
• /
• v.44 no.3
• /
• pp.339-359
• /
• 2022

In this paper, we investigate k-Ricci curvature and k-scalar curvature on lightlike hypersurfaces of a real space form ${\tilde{M}}$(c) of constant sectional curvature c, endowed with semi-symmetric non-metric connection. Using this curvatures, we establish some inequalities for screen homothetic lightlike hypersurface of a real space form ${\tilde{M}}$(c) of constant sectional curvature c, endowed with semi-symmetric non-metric connection. Using these inequalities, we obtain some characterizations for such hypersurfaces. Considering the equality case, we obtain some results.

• Journal of the Korean Mathematical Society
• /
• v.45 no.6
• /
• pp.1577-1590
• /
• 2008

We study Ribaucour transformations on nondegenerate local isometric immersions of Lorentzian space forms into Lorentzian space forms with the same sectional curvatures which have flat normal bundles. They can be associated to dressing actions on the solution space of Lorentzian Grassmannian systems.

• The Journal of Korean Association of Computer Education
• /
• v.9 no.1
• /
• pp.89-95
• /
• 2006

The local geometric properties such as curvatures and normal vectors play important roles for analyzing the local shape of objects in the fields of computer graphics and computer vision. The result of the geometric operations such as mesh simplification and mesh smoothing is dependent on how to compute the curvatures of meshes because there is no exact mathematical definition of curvature at vertices on 3D meshes. Therefore, In this paper, we indicate the fatal error in computing the sectional curvatures of the most previous discrete curvature estimations. Moreover, we present a discrete curvature estimation to overcome the error, which is based on the parabola interpolation and the geometric properties of Bezier curves. Therefore, We can well distinguish between the sharp vertices and the flat ones, so our method may be applied to a variety of geometric operations.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.327-335
• /
• 2005

For a compact and orientable minimal real hypersurface $M\;in\;QP^n$, we prove that if the minimum of the sectional curvatures of Mis 3/(4n - 1), then M is isometric to the geodesic minimal hypersphere $M_{0,n-1}^Q$.

• Proceedings of the KSR Conference
• /
• 2007.05a
• /
• pp.1097-1106
• /
• 2007

Rail provides running tract for train and broadly and widely conveys the weight of the train exerted from the train wheels that the rail directly supports onto the cross tie and roadbed, and supports the cross-sectional pressure exerted by centrifugal force at curvatures. That is, stationary rail provides surface on which dynamic train runs and guarantees cross-sectional resistance to enable the vertical snake motion of the train wheels as well as to maintain lateral force at curvatures. Rail provides running surface on which train wheels can run smoothly, and secures vertical and lateral force. However, it undergoes continuous destructive reactions (wearing and damages) and abrasion of the cladding by the train wheels. It is obvious that wearing will result when two metal parts act against each other. However, occurrence of abnormal wearing such as rapid wearing of the rail side due to complex generation of various mechanisms at the contact surface between the rail and train wheel flange. It is not easy to simply examine the causes of occurrence of abnormal wearing of rail and train wheel flange. Although countless number of academicians and specialists are conducting researches on abnormal wearing of rail and vertical wearing of train wheels, I believe it is too early to argue on pros and cons due to insufficiency of officially verified information on the issue. This review will be focusing on the examples of repairs that reduced the generation of abnormal wearing of rail by reviewing and improving characteristics of wearing and slack, speed of the train and cant as well as status of lubricator by choosing the compound curves present in the section between the $Anguk{\sim}Jongno3-ga$ Stations of the Route No. 3 among the compound curve tracks of the Seoul Metro Routes No. 3 & 4 at which abnormal wearing is generated continuously.

• Journal of Aerospace System Engineering
• /
• v.2 no.1
• /
• pp.7-12
• /
• 2008

The three-dimensional finite element modeling of a composite rotor blade is very hard and requires much computation effort. The efficient method to model a composite beam is necessary for the dynamic and aeroelastic analyses of rotor blades. In this study, the beam modeling method of a composite rotor blade is studied using VABS. The computer program, VABS (Variational Asymptotic Beam Section Analysis), uses the variational asymptotic method to split a 3-D nonlinear elasticity problem into 2-D cross-sectional analysis and 1-D nonlinear beam problem. The VABS can produce the sectional stiffness coefficients of composite rotor blades with various cross section and initial twist/curvatures, and recover the original 3-D distribution of displacement/strain/stress fields. The results of various cross section beams show that VABS gives us the accurate results comparared to commercial codes and does not need much computation effort. It can be concluded that VABS provides the efficient method to establish the FE model of a composite rotor blade.

• Steel and Composite Structures
• /
• v.9 no.3
• /
• pp.275-301
• /
• 2009

The long-term behaviour of simply supported composite steel-concrete beams with deformable connectors subjected to skew bending and torsion is presented. The problem is dealt with by recurring to the displacement method, assuming the bending and torsional curvatures and the longitudinal deformations of each sectional part as unknowns and obtaining a system of differential and integro-differential equations. Some solving methods are presented, in order to obtain exact and approximate solutions and evaluate the precision of the approximate ones. A case study is then presented. For the sake of clearness, the responses of the composite beam under loads applied in different directions are studied separately, in order to correctly evaluate the effects of each load condition.

• Steel and Composite Structures
• /
• v.5 no.6
• /
• pp.443-458
• /
• 2005

Steel angles are widely used in roof trusses as web and chord members and in lattice towers. Very often angle members are connected eccentrically. As a result, not only an angle member is under an axial force, but it is also subject to a pair of end eccentric moments. Moreover, the connection at each end provides some fixity so neither pinned nor the fixed end represents the reality. Many national design codes allow for the effects due to eccentricities by modifying the slenderness ratio and reducing the compressive strength of the member. However, in practice, it is difficult to determine accurately the effective length. The concept behind this method is inconsistent with strength design of members of other cross-sectional types such as I or box sections of which the buckling strength is controlled by the Perry constant or the initial imperfection parameters. This paper proposes a method for design of angle frames and trusses by the second-order analysis. The equivalent initial imperfection-to-length ratios for equal and unequal angles to compensate the negligence of initial curvatures, load eccentricities and residual stresses are determined in this paper. From the obtained results, the values of imperfection-to-length ratios are suggested for design and analysis of angle steel trusses allowing for member buckling strength based on the Perry-Robertson formula.