Torus actions on homotopy complex projective spaces

We prove that an effective action of a torus T on a homotopy P^m is linear if m < 4 rk(T) – 1. Examples show that the bound is optimal. Combining this with a theorem of Hattori we conclude that the total Pontrjagin class of such a manifold is given by the usual formula (1 + x²)^{m + 1}.The second named author is an Alfred P. Sloan Research Fellow and was partly supported by an NSF grant.in final form: 10 May 2003     

Real hypersurfaces of a complex projective space

In this paper, we classify real hypersurfaces in the complex projective space C P^\fracn+12C P^{\frac{n+1}{2}} whose structure vector field is a φ-analytic vector field (a notion similar to analytic vector fields on complex manifolds). We also define Jacobi-type vector fields on a Riemannian manifold and classify real hypersurfaces whose structure vector field is a Jacobi-type vector field.     

Vafa-Witten bound on the complex projective space

We prove that the largest first eigenvalue of the Dirac operator among all Hermitian metrics on the complex projective space of odd dimension m, larger than the Fubini-Study metric is bounded by (2m(m+1))^1/2. Mathematics Subject Classification (2000): 53C27, 58J50, 58J60.     

复射影空间中迷向Kaehler子流形

讨论了复射影空间中迷向Kaehler流形,运用活动标架法获得关于截面曲率,Ricci曲率和第二基本形式模长的Pinching定理,将相关结果作了一定的推广.     

On the first pontrjagin class of homotopy complex projective spaces

Let M ²ⁿ be a closed smooth manifold homotopy equivalent to the complex projective space ℂP(n). It is known that the first Pontrjagin class p ₁(M) of M ²ⁿ has the form (n+1+24α(M))u ² for some integer α(M) where u is a generator of H ²(M; ℤ). We prove that α(M) is even when n is even but not divisible by 64.     

Minimal 2-spheres in a complex projective space

In this paper conformal minimal 2-spheres immersed in a complex projective space are studied by applying Lie theory and moving frames. We give differential equations of Kähler angle and square length of the second fundamental form. By applying these differential equations we give characteristics of conformal minimal 2-spheres of constant Kähler angle and obtain pinching theorems for curvature. We also discuss conformal minimal 2-spheres of constant normal curvature and prove that there does not exist any linearly full minimal 2-sphere immersed in a complex projective space CPn (n>2) with non-positive constant normal curvature. We also prove that a linearly full minimal 2-sphere immersed in a complex projective space CPn (n>2) with constant normal curvature and constant Kähler angle is of constant curvature.     

On monodromy of complex projective structures

Summary We prove that for any nonelementary representation : ₁(S SL (2, )) of the fundamental group of a closed orientable hyperbolic surfaceS there exists a complex projective structure onS with the monodromy .Oblatum IV-1993 & 24-IV-1994     

Almost complex and complex structures on real projective Stiefel manifolds

We give a complete list of real projective Stiefel manifolds which admit almost complex structures and show that many of them are in fact complex manifolds. The first named author was supported in part by Grants 1/1486/94 and 2/1225/96 of VEGA (Slovakia) during the preparation of this work.     

Scalar curvature of a certain CR-submanifold of complex projective space

We study an n-dimensional, compact, minimal CR-submanifold of CR-dimension n − 1 and give a sufficient condition for the submanifold to be a tube over a totally geodesic complex subspace. Dedicated to Professor U-Hang Ki on his 60th birthday This work is supported by the research grant of the Catholic University of Taegu-Hyosung in 1996.