Riemannian submersions from simple, compact Lie groups (2009)
Kerin, Martin, Shankar, Krishnan
In this paper we construct infinitely many examples of a Riemannian submersion from a simple, compact Lie group $G$ with bi-invariant metric onto a smooth manifold that cannot be a quotient of $G$ by...
Conjugate Points in Length Spaces (2007)
Shankar, Krishnan, Sormani, Christina
In this paper we extend the concept of a conjugate point in a Riemannian manifold to complete length spaces (also known as geodesic spaces). In particular, we introduce symmetric conjugate points and...
Snowflake groups, Perron-Frobenius eigenvalues, and isoperimetric spectra (2006)
Brady, Noel, Bridson, Martin, Forester, Max, Shankar, Krishnan
The k-dimensional Dehn (or isoperimetric) function of a group bounds the volume of efficient ball-fillings of k-spheres mapped into k-connected spaces on which the group acts properly and...
Symmetries of Eschenburg spaces and the Chern problem (2006)
Grove, Karsten, Shankar, Krishnan, Ziller, Wolfgang
The known manifolds of positive sectional curvature are either homogeneous spaces or biquotients, i.e. quotients of a compact Lie group by a group acting on the left and right simultaneously. The...
Life-threatening ventricular arrhythmia recognition by nonlinear descriptor (2005)
Sun Yan, Chan Kap, Krishnan Shankar
Abstract Background Ventricular tachycardia (VT) and ventricular fibrillation (VF) are ventricular cardiac arrhythmia that could be catastrophic and life threatening. Correct and timely detection of...
Characteristic wave detection in ECG signal using morphological transform (2005)
Sun Yan, Chan Kap, Krishnan Shankar
Abstract Background Detection of characteristic waves, such as QRS complex, P wave and T wave, is one of the essential tasks in the cardiovascular arrhythmia recognition from Electrocardiogram (ECG)....
Diffeomorphism type of the Berger space SO(5)/SO(3) (2004)
Goette, Sebastian., Kitchloo, Nitu., Shankar, Krishnan.
American Journal of Mathematics - Volume 126, Number 2, April 2004
Spherical rank rigidity and Blaschke manifolds (2003)
Shankar, Krishnan, Spatzier, Ralf, Wilking, Burkhard
Let M be a complete Riemannian manifold whose sectional curvature is bounded above by 1. We say that M has positive spherical rank if along every geodesic one hits a conjugate point at t=\pi. The...
Feature extraction for the analysis of colon status from the endoscopic images (2003)
Abstract Background Extracting features from the colonoscopic images is essential for getting the features, which characterizes the properties of the colon. The features are employed in the...
Diffeomorphism type of the Berger space (2002)
Goette, Sebastian, Kitchloo, Nitu, Shankar, Krishnan
We compute the Eells-Kuiper invariant of the Berger manifold SO(5)/SO(3) and determine that it is diffeomorphic to the total space of an S^3-bundle over S^4. This answers a question raised by K....
Cardiac arrhythmia classification using autoregressive modeling (2002)
Ge Dingfei, Srinivasan Narayanan, Krishnan Shankar
Abstract Background Computer-assisted arrhythmia recognition is critical for the management of cardiac disorders. Various techniques have been utilized to classify arrhythmias. Generally, these...
On complexes equivalent to Formula-bundles over Formula (2001)
Kitchloo, Nitu, Shankar, Krishnan
$${\hbox{ S }}^{3}$$-bundles over $${\hbox{ S }}^{4}$$ have played an important role in topology and geometry since Milnor showed that the total spaces of such bundles can be exotic spheres. Until...
On Complexes Equivalent to $\mathbb{S}^3$-bundles over $\mathbb{S}^4$ (2000)
Kitchloo, Nitu, Shankar, Krishnan
There has been renewed interest in $\mathbb{S}^3$-bundles over $\mathbb{S}^4$ since K. Grove and W. Ziller constructed metrics on nonnegative curvature on the total spaces of these bundles. In this...
Isometry groups of homogeneous, positively curved manifolds /--by Krishnan Shankar. (1999)
Thesis research directed by Dept. of Mathematics.
Krishnan Shankar, J. Geometric Analysis
, OR, May 1993. ffl William Einzig Memorial Scholarship, Reed College, Portland, OR, awarded 1991-92, 1992-93. ffl Presidential Commendation for Academic Excellence, Reed College, Portland, OR,...