TOTALLY REDUCIBLE FOCAL SET WITH STEREOGRAPHIC PROJECTION

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