On surfaces with prescribed shape operator

The problem of immersing a simply connected surface with a prescribed shape operator is discussed. I show that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space of such realizations is a convex set in an affine space of dimension at most 3. The cases where this maximum dimension of realizability is achieved are analyzed and it is found that there are two such families of shape operators, one depending essentially on three arbitrary functions of one variable and another depending essentially on two arbitrary functions of one variable. The space of realizations is discussed in each case, along with some of their remarkable geometric properties. Several explicit examples are constructed.

An identity-based motivational model of the effects of perceived discrimination on health-related behaviors

Perceived discrimination is associated with increased engagement in unhealthy behaviors. We propose an identity-based pathway to explain this link. Drawing on an identity-based motivation model of health behaviors (Oyserman, Fryberg, & Yoder, 2007), we propose that erceptions of discrimination lead individuals to engage in ingroup-prototypical behaviors in the service of validating their identity and creating a sense of ingroup belonging. To the extent that people perceive unhealthy behaviors as ingroup-prototypical, perceived discrimination may thus increase motivation to engage in unhealthy behaviors. We describe our theoretical model and two studies that demonstrate initial support for some paths in this model. In Study 1, African American participants who reflected on racial discrimination were more likely to endorse unhealthy ingroup-prototypical behavior as self-characteristic than those who reflected on a neutral event. In Study 2, among African American participants who perceived unhealthy behaviors to be ingroup-prototypical, discrimination predicted greater endorsement of unhealthy behaviors as self-characteristic as compared to a control condition. These effects held both with and without controlling for body mass index (BMI) and income. Broader implications of this model for how discrimination adversely affects health-related decisions are discussed.