TOTALLY REDUCIBLE FOCAL SET WITH STEREOGRAPHIC PROJECTION

Year 2004, Issue: 006, 231 - 238, 15.10.2004

R. Ezentaş

Abstract

In [1], Carter and the author introduced the idea of an immersion f :M→Rn with

totally reducible focal set (TRFS). Such an immersion has the property that, for

all p∈M , the focal set with base p is a union of hyperplanes in the normal plane to

f (M) at f (p) . In this study, we show that the property of an immersion having

TRFS is preserved under inverse image of stereographic projection.

Keywords

Focal Set, Totally Reducible Focal Set, Stereographic Projection

TAMAMEN İNDİRGENEBİLEN FOCAL CÜMLE İLE STEREOGRAFIK PROJEKSIYON

Abstract

S. Carter ve yazar, f :M→Rn tamamen indirgenebilen focal cümleye (TRFS)

sahib immersiyon tanımını [1] de verdi. Bu immersiyon her p∈M için, p ye bağlı

focal cümle, f (p) de f (M) ye normal düzlemdeki hiperyüzeylerin bir

birleşimidir. Bu çalışmada bu özelliği sağlayan TRFS ye sahip immersiyonlar,

stereografik projeksiyonun ters görüntüsü altında korunduğu gösterildi.

Keywords

Focal Cümle, Tamamen İndirgenebilen Focal Cümle, Stereografik Projeksiyon

References

• [1] S. Carter and R. Ezentas, Immersion with totally reducible focal set, Journal of Geometry, 45 (1992), 1-7.
• [2] A.M. Flegmann, Parallel rank of a submanifold of Euclidean space, Math. Proc. Camb. Phil. Soc., 106 (1989), 89-93.
• [3] J. Milnor, Morse Theory, Princeton Univ. Press, Princeton, 1963.
• [4] R.S. Palais and C.L. Terng, Critical point theory and submanifolds geometry, Lecturer Notes in Maths. 1353, Springer-Verlag, Berlin, 1988.
• [5] C.L. Terng, Submanifolds with flat normal bundle, Math. Ann, 277 (1987), 95-111.